The Premier League champions cannot reach the knockout stages of the Champions League and still need to beat Borussia Dortmund on Tuesday if they are to finish third in their group and drop into the continent's second-tier competition.
And failure would mean a reduced number of games in which Mancini could rotate his vast squad, with his numerous big-name players expecting match time.
"The Europa League has been a failure if you look at the way our league clubs have treated it but I don't think losing is ever healthy for a big club and City need to beat Dortmund," Sir Alex told the Sunday Mirror.
|MONEY FOR OLD EUROPA|
|10/1||Manchester City are 10/1 with William Hill to beat Borussia Dortmund 2-1|
"They are out of the League Cup and the Champions League - and for a club of that size it means they've not got enough games to keep the momentum and the interest going.
"I don't know enough about City's players. I've not worked with any of them, apart from Carlos Tevez. But sometimes players want to play every game.
"I've got that with Wayne Rooney. If he misses one or two games it takes him three games to get back. Some players have to play every week. It's a fact.
"Yes, you'd have them fresh for league games and you would have more time for training, but you would have to deal with the fact that you've not got European football. Every manager wants to do well in Europe - I do, anyway."