Scotland sealed World Cup qualification with last night's 4-2 victory over Denmark.
Afterwards, Robertson paid tribute to former Liverpool teammate Diogo Jota after he was killed in a car accident over the summer.
He said, "That just sums up this squad. Never say die. We just keep going right to the end and one of the craziest games.
"We put the country through it, but I'm sure it's worth it. We're going to the World Cup.
"I've hid it well, but today I've been in bits. I know the age I'm at, this could be my last chance to go to the World Cup.
"I couldn't get my mate Diogo Jota out of my head today. We spoke so much about going to the World Cup. I know he'll be smiling over me today. I'm so glad it's ended up this way."
Robertson also highlighted the leadership and inspiration of Clarke.
The Liverpool fullback continued: "This group of boys, this group of staff - it's the best group I've been involved in.
"The manager's speech before the game was unbelievable. He went through the big moments we've had. Qualifying for the Euros - he couldn't quite remember - we were in Wunderbar. He said 'let's make it another one'.
"We were quite emotional. To do it for him, the staff and all our families, it'll go down as one of the greatest nights of my life."