Carrick made his final United appearance in the 1-0 win over Watford on Sunday, bringing to an end a 19-year playing career that included 12 seasons at Old Trafford.
Veteran midfielder Carrick, 36, is hanging up his boots to take up a position on Mourinho's backroom staff - although that move was planned before news of Faria's departure was announced at the weekend.
The former England midfielder also said he meant to be a "pest" by picking the brains of as many people as possible as he embarks on his foray into coaching and potentially management in the future.
"I am sure if they win the FA Cup then as a fan I would think "yeah, win a trophy, finish second", it's the first time that has happened since Sir Alex Ferguson retired, but then go and win the title".
"I'm going to have assistant coaches, I'm going to have fitness coaches, and a structure where they have specialists in different areas connected to the performance".
"It changes overnight. I am not training this week".
The 55-year-old Englishman was asked by Premier League Daily whether or not Jose will miss an assistant like Faria, to which Phelan replied, "That's a good question". It all fits in.
"The final chance to cut the cloth clean. As soon as this came up I didn't think twice", he said.
He said: 'I need to thank Jose for giving me the opportunity. I am extra excited in regards to the future then wanting again and being unhappy it is over.
"I had the issue when I signed and it was all about Roy Keane, but I was never going to replace Roy Keane because it's not how I am".
He said: 'You've got to go step by step. There will be other players. I always felt comfortable and safe next to him, and he probably didn't get the credit he deserved at the time, but he's starting to get that now. It's not just game to game but half to half.
"I'm not getting ahead of myself". I loved playing with him.
"We want to win next week [against Chelsea in the Emirates FA Cup final] to finish the season in a high".