The Portuguese left after two-and-a-half years at the club on Tuesday morning with the 3-1 defeat to Liverpool at Anfield on Sunday proving his final game in charge.
Ole Gunnar Solskjaer has subsequently been appointed as the club’s interim boss until the end of the season.
Mourinho said: ”I have been immensely proud to wear the badge of Manchester United since the first day I arrived, and I believe all United supporters recognise this. Just as was the case with my previous clubs, I have worked with some wonderful people and I believe that some will be my friends for life.
“I know that you are all aware of my professional principles. Each time a chapter is closed I show my deepest respect and I don’t make any comments about my former colleagues.
“I hope the media will also respect my position and let me live my normal life until the moment I decide to return to football. Merry Christmas.”
Mourinho lifted the Europa League, EFL Cup and Community Shield in his first year at United before finishing runners-up in both the league and FA Cup, but things have unravelled since the start of his third campaign at the helm.
He made his frustrations about players and the club’s decisions clear over recent months, but kept his feelings on such matters to himself when doorstepped near his London home earlier in the day.
It appears that chapter is already closed for Mourinho as he focuses on the future, with talk of a return to Real Madrid a possibility.
“I don’t change,” the Portuguese told Sky Sports News. “What I did when I left Chelsea, for example, is the same that I am going to do now. I keep the good things and I don’t speak about anything that happened in the club.
“We could speak about so many good things, we could speak about not as good (things), but that’s not me. It’s finished.
“Manchester United has a future without me and I have a future without Manchester United, so why should I now be sharing with you or even with the supporters any of my feelings.
“It’s over and that’s me and that’s the way I have always been. I was always very critical of managers that leave clubs and then they come out and they speak about the details of what happened and who is to blame for (it) and this kind of situation. That’s not me.
“I just want to finish, like it happened yesterday, and, as I like to say, it’s game over.
“I just hope you (in the) media respect this way of myself to be, to react to this kind of situation and until I get back to football I think I have to right to live my normal life, like I am going to do now.
“I go for my little shopping, I go for my little walk and that’s what I want to do and Manchester United is (in the) past.”
Mourinho was fired three years and a day after being sacked by Chelsea, who he left for the second time with their dreadful Premier League title defence underpinned by “palpable discord”.
United were in a better state than the Blues on the field, although the 11-point gap to the top four was as concerning as the 19 points to leaders Liverpool after a mere 17 matches.
The style of play on the pitch and continued volatility off it under Mourinho was a concern to the United hierarchy, with the powers that be worried by the lack of development being made with new signings and young players.
Solskjaer will now take temporary charge - beginning with the trip to former club Cardiff on Saturday evening – until next summer, when the club will appoint a full-time successor to Mourinho. Tottenham’s Mauricio Pochettino is the club’s No 1 choice.
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