The 35-year-old hangs up his boots following a 12-year stay at Old Trafford, although he will remain at the club in a coaching capacity.
"For a winner like Michael, to win in his final match has to mean something," Mourinho told reporters.
"Sir Alex [Ferguson] was the smart one to sign him and the happy one to have him for so long. An unbelievable player. Even today, I was telling my assistants that I wanted to take him off to standing ovation but I couldn't because he was the best. Today he just changes office [to take coaching role at the club]."
Carrick made 464 appearances for the club across all competitions, helping them to 18 trophies including five Premier League titles and the 2008 Champions League.