The Reds clinched a 20th league title on Monday night after a 3-0 victory over Aston Villa and this latest triumph was Carrick's fifth as a Red, an experience he will never tire of.
"It is an incredible achievement. Every year we win it just gets more special. The sense of achievement gets greater, for the manager and the club," he told PA Sport and the Manchester Evening News.
"This was a special one this year, the way we ended last year. We could have gone two ways and let it affect us and faded away. But we bounced back. We are proud of all the lads for showing their character.
"We were written off at the start of the season, as we are most seasons, but we have managed to come out on top. It is a special feeling."
Carrick also paid tribute to team-mate Ryan Giggs who has now won 13 Premier League titles. "You keep talking about him but what else is there left to say! It is sensational that he is still able to do that after all this time," added the 31-year-old.
"It is not just physical, it is mental, having the drive and desire to do it every day. The standard he has set is unbelievable. He is a legend. It is a throwaway comment too often. But he is a legend. It is a pleasure to play with him and work with him every day."