Franz Beckenbauer spoke of "one of the most beautiful defeats in Bayern Munich’s history" after they reached the Champions League semi-finals.
A volley executed to perfection by Arjen Robben 16 minutes from the end secured Bayern’s passage after Manchester United had raced into a 3-0 lead on the night.
Ivica Olic brought Bayern back into contention in the 43rd minute and their cause was aided by United defender Rafael’s dismissal for a second bookable offence five minutes into the second half.
"We were asleep at the start and Man U were superior in every aspect," admitted Beckenbauer. "At 3-0, I would not have bet even a cent on Bayern. But they turned it around magnificently.
"Two moments were decisive: the goal for 3-1 from Olic just before the break and then Rafael’s red card. Bayern then played with composure, let the ball roll and Robben then scored a dream goal.
"It was one of the most beautiful defeats in Bayern Munich’s history."
It was Bayern’s first defeat at Old Trafford after two draws and a win, and chairman Karl-Heinz Rummenigge added: "That is the first time we have lost in Manchester, but it is a loss we are happy to accept."
It was not the only defeat for Rummenigge, as Bayern president Uli Hoeness explained.
The pair had made a bet before the game on whether Wayne Rooney would actually play, despite seemingly being ruled out due to injury on the eve of the match.
"Karl-Heinz Rummenigge has got to pay for a dinner with 10 guests," said Hoeness. "We had a bet and I said that he would play."
Unlike Beckenbauer, Hoeness always fancied his side’s chances, even after United’s impressive opening.
"In the stands, we never had the feeling that it would go down the pan," he said on the club’s website. "That is a magnificent thing.
"We played cleverly and just waited for our chance to arrive. What really distinguishes the team and the coach is that they always believe in themselves."
Coach Louis van Gaal was delighted with his side’s fighting spirit.
"I am obviously proud," he said.
"Given that we were 3-0 down, it is incredible what we achieved in the second half.
"We played like a big team. Robben’s goal was unbelievable."
Bayern’s focus now turns to reaching the final for the first time since winning the trophy on a penalty shoot-out against Valencia at the San Siro in 2001.
"It would be fantastic to go one more round," said midfielder Bastian Schweinsteiger.
"We made a pact in the interval that we would go out and play like men. The red card also helped us.
"Manchester have a great stadium with great fans who spur them on. But we held our own against them."