United emerged as late contenders for the ex-Arsenal contract rebel and managed to secure his services after they persuaded the north Londoners to conduct a swap deal involving Armenia captain Mkhitaryan.
And on rumours about Cristiano Ronaldo returning to United, Mourinho said: "Real Madrid is a club I care about, so I am the last one to add [to the] fire".
"Now we have five attacking players of quality, Mata, Rashford, Lukaku, Martial, Alexis and it's fantastic for me and for the team, if the players one day are on the bench and they don't like it, I'm happy with that", Mourinho added.
Mourinho was initially handed a three-year deal when he took over from Louis van Gaal and has now signed on for a further 12 months at least.
"His work rate and professionalism are exceptional and he has embraced the club's desire to promote top-quality young players to the first team".More news: Arsenal have bid for Pierre-Emerick Aubameyang rejected by Borussia Dortmund
"Here at Arsenal I know that lots of players move a lot and it's incredible the way [the team] plays".
City won't lose sleep over one transfer, however, and now lie 12 points ahead of their city rivals at the summit of the Premier League after 24 matches.
"Could he have performed better?" The Portuguese also said that he has more attacking players option now. "Maybe. But I don't have regrets".
"I've known him for many, many years, I was with him in Italy at Udinese, in Spain, when he was at Barcelona, in England, when he was at Arsenal, so our careers were nearly made in the same countries simultaneously, so I know him very very well". "We are very happy with this transfer from Manchester United".
'That was one of the things that attracted me to come here, along with the manager, who is a person who won everything in Italy, the same as he did in Spain.