Mancini has presided over a hugely disappointing campaign, with City finishing bottom of their Champions League group and currently trailing United by 15 points in the Premier League.
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“If a manager doesn’t win for a few games then he will hear all kinds of stuff,” the Scot told reporters.
“It goes with the territory and Mancini will know that. I don’t think he’ll be worried about that. He knows what he’s capable of.
“I don’t see any reason why Mancini won’t be there again next year.”
City have been accused in some quarters of lacking the hunger to defend their Premier League title, and Sir Alex admits the pain of last season's failure is driving his team on to new heights.
“It’s hard to retain the title,” he added.
“We were disappointed last year because of the way we lost it. So we’ve had that focus.
“The concentration, the team spirit, has been brilliant. So these are all advantages. We had the advantage of trying to recover from the disappointment of last season.
“We have 26 players and you can only manage them if the players themselves buy into it. They have to understand changes have to be made. That is why we’ve been successful.”