Ole Gunnar Solskjaer said Manchester United always make it hard for themselves.
They did just that here, but even with their famed comeback ability, this was one escape act too far, despite plundering two late goals to give them hope.
Needing a point to advance to the last 16, United found themselves 2-0 down after 14 minutes and tumbling into the Europa League after the briefest of stays at European football’s top table.
Having won their opening two group games, United were in control of their fate, but a shock loss at Istanbul Basaksehir started the rot that saw them end with successive defeats to go out.
Two late goals in as many minutes from Bruno Fernandes and sub Paul Pogba gave United hope of snatching the equaliser they needed, but ultimately they left themselves with too much to do.
Just as he was in the 3-1 home defeat to Paris St Germain last week, when his failure to hook Fred before his inevitable sending off condemned United to defeat, Solskajer was wholly to blame.
Despite saying United would go out to win, Solskjaer set his team up not to lose and paid the price for his cautious team selection, Leipzig taking full advantage of their opponents’ uncertainty.
And when a change of formation and personnel was urgently required with United 2-0 down and 32 minutes of the first-half remaining, Solskjaer dithered and waited until the break to make changes.
Five years to the day United slumped to a shock 3-2 defeat at Wolfsburg to exit the Champions League, Solskjaer’s side endured the same fate, with only themselves to blame.
They got off to the worst possible start, conceding after just two minutes, their defence undone yet again and made to pay for their disorganisation.
Leipzig skipper Marcel Sabitzer spotted the run of Angelino and dispatched a perfect delivery for the on-loan Manchester City man, who scored with a thumping Roberto Carlos-esque finish.
It was Angelino’s seventh goal of the season, the left-back grateful to United full-back Aaaron Wan-Bissaka, who showed his defensive naivety by failing to spot his run behind him.
Things went from bad to worse for United in the 13th minute, Angelino again afforded space to cross for Amadou Haidara to apply a volleyed finish to make it 2-0.
Emil Forsberg should have made it 3-0 two minutes later, but prodded the ball wide from close-range, United proving obliging opponents once again by standing off him.
Peter Gulacsi kept United at bay with a succession of fine saves after the break, while Bruno Fernandes hit the bar with a free-kick in the 68th minute. A minute later and it was 3-0.
A calamitous mix-up between De Gea and Harry Maguire allowed sub Justin Kluivert to nip between them and score.
Fernandes gave United a lifeline with a penalty 10 minutes from time and sub Paul Pogba pulled a second one back two minutes later, to ensure a frantic finale.
United came agonisingly close to the third goal they needed in added time when Nordi Mukiele turned the ball towards his own net, but straight at Gulacsi.
Yet United did not deserve to go through, despite their late rally, and now the painful inquest begins for Solskjaer.