The fullback has left Liverpool for Real Madrid ahead of the Club World Cup.
Moore also offered detail on how Liverpool management will have handled the new contract talks of Virgil van Dijk and Mohamed Salah.
He told talkSPORT: “I've been gone a few years but the issue is Trent, Mo and Virgil coming to the end and the PR issues," Moore said. "You have the agents yapping in the background trying to put pressure on the club. All of that, Liverpool handled very well.
"Ramy Abbas is very seasoned now, Mo is his No.1 client, how do we announce things that don't put Trent under pressure for announcement and how does Virgil, as the captain, announce things? All of those have to go together.
“It was pretty clear he said to Arne at the start of the season that I'm out of here but I'm going to give you everything now because he's such a good kid. What do I know, but Arne probably said I need you to bring Conor (Bradley) along because this kid is going to be 30-35 games a season in your position. Virgil and Mo, I think, knew what was going on so were nonplussed about the drama. This is where social media kicks in."
Never panicked
Moore also stated: “Liverpool has always been this way and we arrogantly call it the 'Liverpool way' where we're just going to get business done, there's not going to be a lot of drama and, when I was there, there was a conversation with agents that if you're going to start doing this to the media to try to manipulate the situation or change the narrative to advantage your client, we're not going to give in."
On Salah speaking out on his contract situation during the season, Moore added: “I know his agent, I know Mo. It was with the mixed media, which was weird. I think Ramy, his agent, probably said go and have a word, kick things along but all's well that ends well.”