They need to overcome a 3-0 deficit in their quarter-final, second leg against Liverpool at the Etihad Stadium.
"Contratulations to United. Now we will try, if we are fearless enough, to stand up again and focus on Tuesday", said City manager Pep Guardiola.
His shots at Champions League glory in his first two seasons at Bayern Munich were also ruined by three goals in quick succession for Real Madrid and Barcelona in the semi-finals.
"I went to congratulate him on the result", he said, offering no more insight into the exchange.
"In Barcelona (against Bayern in 2015) 71 minutes (it's) 0-0, (at) 90, 3-0. I think, much. much more".
Goals from Vincent Kompany and Ilkay Gundogan put the Premier League leaders ahead in the first half, then Raheem Sterling could have, and really should have, increased City's lead when he squandered two one-on-one chances against David De Gea.More news: Pittsburgh Pirates vs. Chicago Cubs, 4-9
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And in a recurring theme of his near two-year reign at City, Guardiola insisted his side needed to be more clinical rather than changing their style of play.
"But maybe we will improve for the future on that, to realise that sometimes it's not enough what you've done to win the games".
He said in the aftermath of a frustrating afternoon on home soil: "For the fans it is tough and maybe we are going to get more credit if we are able to win the Premier League and people will say how tough it is to win".
"We make a good performance in the second half".
"We were not good enough in the end".
"You'd have to say they probably would".
And Guardiola believes City have to reach the standard set by the likes of Cristiano Ronaldo and Lionel Messi if they are to break through as a European powerhouse. "The schedule is like this, that's why this competition is so tough", Guardiola said. So when you have the chances you have to score two and it's possible that we could've scored three.