Mourinho made nine changes from Thursday's goalless draw at West Ham, Scott McTominay and Alexis Sánchez surviving.
But there was still a moment to remember late on as Carrick's 464th United appearance came to a close, receiving a standing ovation as he was replaced by Paul Pogba on a day that belonged to one of the club's most distinguished servants.
The likes of Richarlison, Deulofeu and Andre Gray were looking particularly risky in the opening exchanges which gave the travelling supporters hope that they could achieve a positive result on their final outing of the season.
He then sarcastically hit out at his critics as he suggested the negativity around the team was not justified: "If you want to be negative, you can be negative until the point that you can say that Scott McTominay is not good enough", he said.
Mourinho said: "He was injured, he was injured Friday training session, yesterday [Saturday] couldn't train. He had treatment at the training ground", added the United boss.
"I don't know [when he will return]".
With second place already secured, Sunday afternoon was all about Michael Carrick for everyone associated with Manchester United. I know the style sometimes frustrates the fans but you can not argue with results.
Carrick said: "I have to thank the manager an terrible lot".More news: Israeli rights groups rebuke plan to deport Human Rights Watch directo
Carrick spoke to the fans after the win, thanking them for all their support over his 12-year career at the club, where he has lifted every trophy possible.
"It's hard because he is my friend, 17 years is a long time", Mourinho added.
"I think if you're looking at the City game now. We will give everything we can to bring the FA Cup back here next week".
He also sent out best wishes to former manager Sir Alex Ferguson who is in hospital recovering from a brain haemorrhage.
"It's been a tough week for everyone at the club".
Mourinho told a news conference: "It is hard because for me these two seasons I got him in the last period of his career when it was hard for him to play consecutive matches at higher intensity; never a big injury thankfully, but little problems were coming now and again and when he was ready for more, a little problem was coming".
"We want to see him sitting back up there some time soon".