The 36-year-old former England midfielder ended his playing career against Watford on Sunday after 12 seasons and 464 appearances for United.
"I would like to thank him for the opportunity and confidence, for the knowledge and experience, but most importantly for his friendship", he said.
Marcus Rashford scored the only goal after a pass from Juan Mata, to seal the 25th win of the season and get Manchester United to 81 points in 2017-18.
While Carrick might be hanging up his boots, his United team-mates still have the FA Cup final against Chelsea to prepare for.
Nevertheless, United will be losing one of the very best, with Mourinho announcing that he will not be hiring a new number two next season.
Mourinho stated: 'I've to make the selections however in fact my assistants have an opinion.
Manchester United's Michael Carrick says he switched "overnight" from being a player to a coach in readiness for Saturday's FA Cup final at Wembley. I look forward to learning and working closely with him.
Mourinho added: "I will miss my friend and that is the hardest thing for me, but his happiness is more important and, of course, I respect his decision, especially because I know that we will always be together".
I have nobody in the world of football ready to be my assistant manager, so I prefer to educate people and to structure my staff in a way where there is education and improvement.
"That's the measure of the club and has been for 60, 70, 80 years, it has to be the league title you are measured by. I've been at this club, and it is such a great club, so I obviously know the club and the manager", he said.
Jose Mourinho has picked out that player and it's, surprise-surprise, Anthony Martial.
"He's injured", he said. "He had treatment in the morning in the training ground and stayed away".
Watford: Gomes, Janmaat, Cathcart, Kabasele (Mariappa, 20 mins), Holebas, Doucouré, Hughes, Deulofeu (Deeney, 63 mins), Pereyra, Richarlison, Gray (Chalobah, 72 mins).