The Scot announced on Wednesday that he is to retire from football management at the end of the season, calling time on a career which has seen him win 49 trophies across three clubs and 39 years.
And Carrick, who himself has won twelve trophies under Sir Alex since joining United in 2006, believes the 71-year-old's achievements will never be matched.
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"Just look at what he’s achieved - all the titles, all the trophies. I don’t think anyone can match him and I don’t think anyone will.
"He has created an incredible legacy here and it’s his winning attitude that has rubbed off on everyone at the club. To do it year after year for so long is just incredible. What he’s done, what he’s achieved, is just amazing."
After losing the title on goal difference to neighbours Manchester City last season, Carrick admitted he feared a repeat this term.
But, after winning a 20th league title, the 31-year-old has spoken of his pride that he and his team-mates reclaimed the league crown from their city rivals, and is not expecting their success to end following Sir Alex's departure.
"It is a great achievement. Every year we win, it just gets more special. The sense of achievement gets greater, for the manager and the club," Carrick added.
"It was a special one this year, considering 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 and I believe there is a lot more to come from this side."