Club bosses sacked the Portuguese manager on Tuesday following a 3-1 defeat at Anfield that left the 20-times champions an embarrassing 19 points behind league leaders Liverpool after just 17 matches.
Former United striker Ole Gunnar Solskjaer was announced as Mourinho's temporary replacement on Wednesday as the club begins its search for a permanent replacement.
Mourinho lifted the Europa League, League Cup and Community Shield in his first year at the club 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.
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The United boss has made his frustrations about players and some of the club's decisions clear over recent months but kept his feelings on such matters to himself in a statement released the day after his sacking.
"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," Mourinho said in a statement released to Britain's Press Association.
"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.
Reaction to sacking of Manchester United manager Jose Mourinho
"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."
The former Chelsea, Real Madrid and Inter Milan boss told Sky Sports News he has a future beyond United.
"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. That's me and that's the way I've always been and I was always very critical of managers that leave clubs and then they come out and they speak about details of what happened and who is to blame for this kind of situation -- that's not me. I just want to finish, it happened yesterday and I'd like to say it's game over."
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