The former midfielder stepped down as a coach at Old Trafford after overseeing the 3-2 win over Arsenal.
Signed from Tottenham in 2006, the midfielder won a Champions League and five Premier League titles during a medal-laden playing career with the Old Trafford giants.
Carrick joined Jose Mourinho’s coaching staff after retiring in 2018 and then worked under Ole Gunnar Solskjaer who he stepped in for following the Norwegian’s exit last month.
The 40-year-old oversaw the 2-0 Champions League victory at Villarreal and 1-1 Premier League draw at Chelsea, before beating Arsenal 3-2 at a rocking Old Trafford.
Thursday’s match proved his last as a United employee, with the club announcing immediately after the game that Carrick had stepped down ahead of interim boss Ralf Rangnick taking charge.
“It’s 15 and a half years I’ve been here now and it literally takes over your life,” the departing first-team coach said. “It should do as well.
“I’ve dedicated everything I could possibly do as a player and then obviously as a coach.
“I promised my family when I was playing that after I’d finished playing, because you put so much into it, that I’d retire and we’d have a bit of time together. It never happened, I came straight into coaching.
“Just in kind of recent days, it’s just that feeling that the timing’s right, it feels right.
“It’s not been easy to make the decision in that respect but in terms of family and how I feel right now I’m really content and happy and looking forward to what’s ahead.
“It’s a rollercoaster, it’s been amazing. I’ve had incredible memories, some special nights.
“Tonight was obviously special but tonight wasn’t about me. It was the players and the fans, experiencing them type of nights which we should do.”
United fell behind to a bizarre Emile Smith Rowe goal on Thursday, before Bruno Fernandes levelled and Cristiano Ronaldo put the hosts ahead.
Martin Odegaard levelled before Carrick’s former team-mate Ronaldo wrapped up a thrilling 3-2 victory from the spot in front of watching Rangnick.
Asked when he informed players and staff, the caretaker boss said: “I told the coaches, the immediate first-team coaches, today at around lunchtime and then I told the players straight after the game.
“I didn’t want anything to be about me today. It was all about the players and getting the right result.
“I told them straight after the game in the changing room. It was emotional obviously, probably caught them off guard a little bit, but it’s a terrific group of players and I’m sure they’ll go onto great things.
“I’ll be supporting them. I’m not going anywhere, I’m still here, I’ll be supporting them home and away.
“My son is driving me mad to take him to an away game again. I’ve told the players I’ll be right behind them.”
Carrick made 464 appearances for United and leaves as a club great, with football director John Murtough praising his impact as midfielder and then coach.
“He will always be known as one of the finest midfielders in the history of Manchester United, and, more recently, as an excellent coach who has worked tirelessly under two managers to help develop the strong squad which Ralf will now take charge of,” he said.
“We are grateful for the steady leadership Michael has shown through this period of managerial transition, and, while he is now stepping away from day-to-day involvement, he will always be welcome back as a legend of the club.”