Kingsley Coman celebrates his goal against Manchester United.
Erik ten Hag’s side, beaten 3-0 at home to Bournemouth in the Premier League on Saturday, needed to beat the Bundesliga champions and hope that there was no winner in the other group game between Copenhagen and Galatasaray.
And even though Bayern were already comfortable winners of Group A, United were still unable to fulfil their part of the bargain on a night of bitter disappointment.
United were already handicapped by first-half injuries to England duo Harry Maguire and Luke Shaw, with news filtering through that Copenhagen were ahead in Denmark.
Bayern sealed their fate by scoring the winner with 20 minutes left.
England captain Harry Kane, inevitably, was involved with a deft touch to release Kingsley Coman, who easily beat exposed United keeper Andre Onana in front of the Stretford End.
United won just one of their six group games in the competition and defeat against Bayern means they also missed the chance to drop into the Europa League by finishing third.
In the other match in Group A, Copenhagen held on to beat Galatasaray 1-0 to qualify for the last 16.
Manchester United’s tame European exit
The smattering of jeers that greeted the final whistle as United slid out of the Champions League, and indeed all European competition for this season, mirrored the mood of resignation that hung over Old Trafford long before the final whistle.
Anyone who expected United to come out swinging in an attempt to overturn the odds and reach the knockout stages would have been sorely disappointed as Ten Hag’s team were timid and toothless, mustering a miserly single shot on target against a Bayern side who did not have anything to play for.
The injuries to Maguire and Shaw, watched by England manager Gareth Southgate, did not help United’s cause but this cannot be offered up as an excuse for a performance desperately lacking in quality, inspiration and creation.
Bayern’s veteran goalkeeper Manuel Neuer was untroubled throughout, with all the pace and threat on offer on a low-key night coming from the Germans, who were rewarded for their superiority with Coman’s winner.
The space and time afforded before his finish almost embarrassing.
Rasmus Hojlund had a chastening sight, running tirelessly without any service and being outmuscled comprehensively by Dayot Upamecano and Kim Min-jae. The Dane was bent over exhausted and beaten seconds before the final whistle.
When the draw for this group was made, United must have relished their return to the Champions League but it has been a harrowing experience.
They came up short on the twin faults of a team that is not fit for purpose and also only too happy to engineer their own downfall, as they did when conceding two-goal leads to lose in Copenhagen and draw away to Galatasaray.
United now have all the feel of a club in crisis with Ten Hag under serious scrutiny and the prospect of a tough trip to Liverpool on Sunday, with Maguire and Shaw likely missing through injury and captain Bruno Fernandes suspended.