Carrick, who is unlikely to be picked for Saturday's FA Cup final against Chelsea on Saturday and will assume a coaching role at United next season, was treated to a guard of honour by both teams before kick off.
But Mourinho insisted his absence was purely down to an injury that could also see him miss next Saturday's showpiece.
The club's greatest ever manager continues to receive hospital treatment following a brain haemorrhage last weekend but is out of intensive care after responding well to surgery.
"My heartfelt thanks go to the manager, Jose Mourinho, for the belief he had in me, all those years ago, when it all was just a student dream". "I think it will be Michael Carrick in the future", he said.
Yaya Toure pleased to leave Manchester City with 'United in the shadow'
City are due to celebrate their title success on Monday with an open-top bus parade through the streets of Manchester. Manchester City's achievement is one that is not matched in the annals of the English top-flight.
"I've been so lucky to play with him for years and hopefully I can enjoy him as an assistant". "I am going to have assistant coaches, I..."
It is believed that Faria is looking to kick-start his managerial career in the 2018-19 season, but that leaves United without an assistant manager and Mourinho without his second-hand man. However, I have felt for some time that I would like to spend much more quality time with my family before pursuing any new challenge in my professional life.
Faria is one of the names who have been linked with filling the large vacuum being left by Arsene Wenger at Arsenal. "We had better performances than results", he said. "I've already spoken many times with the owner, I can feel he is ambitious and he is looking forward for next season". And the reality of the numbers is that between second and fifth, there is three or four or five points, I don't know.
"I'm sure the owner will try to improve the level of the squad and the team, try to improve the position in the table".