Having said that, David Moyes' men, who have no chance of qualifying for next season's Champions League after a poor defence of their Premier League title, had their fans dreaming – briefly – of glory in the competition after Patrice Evra scored a wonder goal to put United 1-0 up on the night and 2-1 ahead on aggregate.
But their joy lasted just 22 seconds after the restart as Bayern, the defending European Champions, hit back through Mario Mandzukic.
Further goals from Thomas Muller and Arjen Robben ensured it would be another dismal night for Moyes, but this spirited performance may just be enough to keep the under-fire manager in the job for another season.
Moyes said his team were guilty of "schoolboy defending" after putting themselves in with a chance of a stunning result.
"It's the sort of thing you learn as a schoolboy once you score a goal, make sure you don't concede," the United manager said.
"You get into position and do your job. We had concentrated so fabulously well throughout the game. The players had done tactically well. Their positioning was good and they did their jobs.
"For us just to give it up on that moment, the goal up, was really disappointing."
Moyes was left to lament his side's defending after they had put themselves in such a great position, but argued there was not too much in the game.
"It was probably 30 seconds after we scored," he said. "You're told as a schoolboys not to concede right away but we conceded too quickly and it was always going be a tough night. I think we need to give ourselves five or 10 minutes but they went right up the other end and scored.
"I don't know if it was about concentration. We were thrilled with the goal but we have enough experience. I didn't think we did an awful lot wrong tonight. We played ever so well and our performance really pleased me but a couple of small errors cost me."
Moyes pointed to two deflections in the build-up to Bayern's third, claiming luck was against his side, but either way Moyes now faces a long summer of rebuilding without the lure of Champions League football to offer new recruits.
"We've not got Champions League football but I believe its not far away and hopefully it's only one year," he said. "We've got to rebuild and our focus now is getting a team together to get back in this competition because it's a really good competition and we've really enjoyed it."
Moyes insisted he had never been told that Champions League qualification was a minimum requirement in terms of his job security or in terms of his transfer budget for the summer.
"That's not a question for me," he said when asked about his job. "My job is just to get on with my job and my focus is on getting a side together to get back in the Champions League. That's our main objective now."
Bayern boss Pep Guardiola said: "I knew it would be hard. It's not easy to play against a team when they have eight players in their box. It happened in Manchester too.
"We decided to create a bit more passing in midfield and get the ball wide. They defended well, but when it got to 1-1 we played much better and we deserve to be in the semi-finals."
Bayern will find out whether they draw Chelsea, Atletico Madrid or Real Madrid tomorrow.
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