Poyet, 57, also draws on how he was sent to scout a certain Virgil van Dijk while Brighton boss and what's best for Uruguayan compatriot Darwin Nunez, with his Liverpool future unclear.
Enzo Maresca took over Chelsea this season. What have you made of his impact so far, and can you see him as a long-term fit at Stamford Bridge?
"I like him, I like many things about him. I think he knew what he needed to do. And then, like I said, it was a moment, I think it's around November, December, that Chelsea lost a little bit of shape and form.
"Then, you learn the most as a coach, you learn which players drop dramatically, which players you need to, you know, you need them to represent you better.
"You need to be stronger in a certain part. For example, I remember watching the good spell (Noni) Madueke, and I said, 'Wow'. And then I didn't see him for four months.
"For Maresca, I think that next season is the key for him. He knows everything, and I really, really hope he will succeed. He looks to me like he has a character."
John Terry came from the academy back then. Did he instantly show those leadership skills and qualities?
"Look, from the first time he came up and trained with us, he was already a strong character because he didn't hold back. Whether he was marking Gianluca Vialli or was marking anyone in there, he would put himself about. I think he's a very intelligent person.
"He had two central defenders in front of him, Franck Leboeuf and Marcel Desailly, who had different characteristics. John, knowing his ability, tried to take the best things for his ability from both. Franck Leboeuf was an exquisite player. We know his right foot, he would ping the ball from right to left. He was a penalty taker. He was doing so many things well, covering at the back.
"Marcel Desailly, an animal, so strong and powerful. I mean, scary. You wouldn't like to fight against Marcel Desailly. And John Terry behind them, watching, training. He got the pinging right and left foot even better than Franck. Also, the aggressiveness, the leadership, and the scary part of Marcel Desailly.
"When I left, I knew he would be playing for many years for Chelsea. And because he was already a character, I was not surprised when he became the captain."
You were at Brighton at a very different time. How amazed are you at their rise and Tony Bloom's bold analytics approach? How was your time there and your relationship with him?
"He was the one I had the best understanding with. He was spectacular with our recruitment system. Obviously, it was his first job as a chairman, and for me, his second manager, a different character.
"Then all the people who went to the club, they started talking to him, and they confused him a little bit about me. But we grew up together. I think he went to another level in terms of not only recruiting players, but recruiting managers.
"I know personally the manager of Brighton now, Fabian, because I had a player from Greece playing for his team in Germany, in St. Pauli, and I went to see the player, and he allowed me to go to the hotel.
"He started talking about football, and he was amazing. I mean, I was I was sitting in there, I'm thinking, 'I would like to play for this guy'. Really, it was so intense. And, and I told him like five times, 'Coach, listen. You are playing tonight. If you wanna go to your room, go'. 'No, no, no, no'. And he kept talking, it was incredible.
"And then there is something that I can put the medal on myself, but there is a way of understanding football in Brighton that we changed. Brighton was a very old football style, English style, long balls, bound fighting and crazy football, and we changed it.
"And it was a culture there. I mean, I don't know how many times I turned to the fans and say, 'Come on', because they wanted the ball forward. And then, they started loving it. Now they say, 'Oh, Brighton, we play football'. I'm thinking, two years ago, you were killing me because you wanted the ball to go long, you like it now?
"We were playing in a rubbish place with only 7,000 people. We won the league, we went up to the Championship, we moved to the new stadium, and we went from 7,000 people to 22,000
"And then during the second season in the Championship, we went to 30,000. I mean, the growth of the team was amazing."
How do you see Brighton's future?
"I cannot tell you what the roof is. I would say this team is gonna be between fifth and 10th all the time. I cannot see them below 10th.
"Especially because I know the chairman. Yes, he's going to buy a player for 15 million. Yeah, he's going to buy a player for 20, but he's not gonna go for 70."
But if we're talking about fifth place, we're talking even Champions League potential.
"He will try. Tony Bloom will try. The chairman will try. I don't know the rest. They have already played Europe. I remember watching the game against AEK, my other previous team. They, They already have that feeling of playing in Europe, which is amazing.
"Imagine, for the fans. I am still meeting certain fans in England, and every now and then, in the underground, they say, 'I'm from Brighton. I went to see you in Yeovil away, you know, like a horrible place in League One, and now I'm going to Europe to Athens'. So, I mean, they went all the way."
You've previously referred to your time there as a manager as the best time in your career, despite the unfortunate ending. Do you envision yourself returning to the club someday, or is it like an entirely closed page for you already?
"It doesn’t depend on me. People from Brighton, and I'm also convinced that Tony Bloom thinks the same. I think his family and I think that half of the board, all the players and all the fans are gonna adapt.
"They know how important we were and that we will always be welcomed there. Now, some people want power, and when you have the power, they don't want you. It was my first job as a main coach.
"Slowly, without me thinking, the chairman gave me power. And with my character and the way I am, I was taking it. I cannot tell you if I liked it or not. It was me. I was taking it.
"Now, the day they sent me that letter that they wanted to disciplinary hearing and all that, sorry about the language, bull****. I realised, I think I got too much power.
"So, I got to a point where somebody in the club went to the chairman, said, 'Huh, he's becoming big and we need to cut him'. You know? Like a tree. Boom. Cut it through, because if we don't cut it through, he's going to take over."
And how much are you data-driven as a manager? Because football is evolving all the time, especially with AI and all the data.
"I don't use it as a first tool. I learned to use the data, for example, let's go to a player. I'm watching a player now, I need to bring him.
"The best person I have worked with on this kind of information is Tony Bloom. He's absolutely unbelievable. It will take you months to learn it because it's so many numbers that you don't imagine. But when you understand why, wow, wow.
"I got great examples of that. One day, I got to the training ground, and I got a phone call from (Bloom). He said to me, 'You need to travel to Groningen to watch a central defender'. And I said, 'What?' 'Yeah, you must go now. Go back, get to the airport, get your passport and go'. And we went with my assistant.
"We sat down in the stands with a little luggage between our legs. Watching the game, and it was Virgil van Dijk. He was of a different class.
"We called (Bloom) back after the game and said, 'Sign him'. But the price was three million, and we were Brighton and we couldn't pay three million for a defender, and we didn't sign him. Then he went to Celtic and then to Southampton.
"But (Bloom) was that kind of guy who was ahead of the rest. He knew that Van Dijk was a player who played in the first division of Holland with those characteristics, with those data, etc."
Your fellow Uruguayan, Darwin Nunez, hasn't fully settled at Liverpool. Does he need a fresh start somewhere else to truly reach his potential, or is patience required?
"It's a very good question, and I got it clear. I think he needs to decide what he wants for his career. He knows his position at Liverpool.
"You know, he's not the type of player that you can say, 'No, next year I want to be the number nine'. No, you are not going to be the number nine. You know your position, okay? You're going to be a player, a squad player that you're going to have your moments, but then when the best team have to play, you're not gonna play. Simple. That's clear, come on.
"There's no lie to ourselves. So it depends on how you feel and your family. If you, if you have family and you feel okay being in that situation, living in where you live and the education of your kids, you can stay, okay?
"Now, maybe you want to play every week. Then you need to move. So, it's, it's very personal that. It's not for everyone, but the most important is that now he knows his position in that squad."
But in terms of his playing style, do you think a possible move to another league, La Liga or even Serie A, would be a better step?
"It depends on how the team plays. Darwin needs his space to use his power and to use, you know, his, his running.
"He cannot play in a team that the other, the position is really low and there, there are little spaces."