Sanchez was close to signing for City in a deal reported to be worth £60 million on transfer deadline day in August, only for Arsenal to block the move when they failed to bring in a replacement.
City were back in for Sanchez when the January transfer window opened only to reportedly baulk at the fees and wages involved, allowing United to move in.
Henrikh Mkhitaryan moved to Arsenal as part of the deal but Mourinho - who signed a contract extension to 2020 at United on Thursday - gave an insight into how close Sanchez was to going to City instead.
"I want to make it clear it was not me," Mourinho told MUTV of the Sanchez transfer. "Totally the credit is for the owners and the board. They did it - a player like Alexis Sanchez.
"It looks like it is difficult for people to say, 'Well done, you did it in a fantastic way'. He was with one-and-a-half feet in another club.
"It looks like it is hard to give credit when we win matches there is always an 'If'. When a player does fantastically well there is always a negative. But the reality is without Manchester United the industry would be in trouble, this is part of being at such a big club."
Mourinho, who brings up his 100th game in charge of United at Yeovil Town in the FA Cup on Friday, made headlines last October when he seemed to openly talk about the prospect of leaving Old Trafford, with Paris Saint-Germain among the clubs reportedly interested.
But the Portuguese coach clarified that he is not intending to leave, merely that he believes it is hard in the modern era for managers to follow the likes of United legend Alex Ferguson in establishing a long legacy at a club.
"I am here for a long, long time but I started really, really young, I'm not as old as people think," Mourinho said. "I'm 55 [on Friday] but I feel myself that I am very young.
"So when a few months ago I told impossible to end my career at Manchester United what I was trying to say is that modern football it is almost impossible to stay 10-15 years.
"I was not saying I was going to leave but I want to work 10-15 years more. I like to do it and I don't see myself doing another thing."