Carrick joined United from Spurs in a £18.6million switch last summer.
Carrick said: “Maybe I did prove people wrong. But you can’t think about doing that or it will distract you from your job.
“I know it was a massive move for me but I always believed in myself.
“In fact, I felt more like a United player the longer the season went on.
“I had to get used to the way we play and the different expectations and pressures from what I was used to.
“But if someone said at the start of the campaign I would have a championship medal, play over 50 games and score six goals I’d have taken that.
“Having said that, playing with the players here I always believed we would win the League.
“Going through what I did last season was a great experience. I now know how hard it is to win a title and it was special to do it in my first season.
“But we are not satisfied we have to keep going and keep improving.
“Last season I learned a lot along the way from the likes of Paul Scholes, Gary Neville and Ryan Giggs about just what it takes to win a title.
“They have been there so long and achieved so many things.
“Those players always look forward and not back and that’s what people like myself have to do now.”