The Red Devils returned to England with their tails between their legs as David Wagner’s men caused an upset in Bern.
Manchester United started on the front foot and took the lead through Cristiano Ronaldo just 13 minutes.
The hosts gained confidence and started causing problems to the Englishmen when defender Aaron Wan-Bissaka was shown a red card for a bad tackle 15 minutes before the interval.
Young Boys got their deserved parity midway through the second half courtesy of Cameroon midfielder Moumi Ngamaleu.
Wagner’s men snatched the maximum points in the dying embers of the game when an error from substitute Jesse Lingard allowed Theoson Siebatcheu to slot home from close range.
"I thought we could have done better in the first half with 11 men, but we always knew they were high intensity, energetic, athletic team and I thought we started OK,” Solskjaer said after the game.
“But we didn't get the second goal that would have killed the game off. In the second half, we felt in control without the ball. They didn't create any big chances, but there were two unfortunate goals.
"That's football for you at the highest level. A lack of concentration, make a mistake and you get punished. We did that last year in Europe, we conceded two very sloppy counter-attacks against Istanbul and we lost that game.