Celtic were left heartbroken after a 94th-minute equaliser from Bayern Munich at the Allianz Arena sent them out of the Champions League on aggregate.
Trailing 2-1 from last week's defeat at Parkhead, Brendan Rodgers' men put on a valiant display to go toe-to-toe with the Bavarian giants.
And they were rewarded for their endeavour when former Bayern player Nicolas-Gerrit Kuhn opened the scoring after taking advantage of a defensive mishap in the second-half.
Celtic looked like they were going to force Bayern to extra-time on Tuesday night but a last-gasp goal from Davies saw exuberant celebrations inside the Allianz Arena.
Alphonso Davies scored what turned out to be the pivotal goal in the 94th minute
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Former Crystal Palace star Michael Olise sent in a teasing cross in the 94th minute which was met by Leon Goretzka.
However, the Germany international's header was brilliantly saved by Kasper Schmeichel at point-blank range.
But the rebound fell kindly for Davies, who threw himself at the ball as Cameron Carter-Vickers tried to clear it.
It saw the ball bundle over the line and, while it was not pretty, it saw Bayern progress to the last-16 of the Champions League.
Whereas Celtic, who had put up a brilliant fight from minute one, were sent packing - having sniffed a famous night in Munich.
Schmeichel, who had on several occasions denied Bayern from equalising in heroic fashion after nine saves, was left motionless at full-time - staring up at the sky as German fans celebrated wildly around him.
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As for star man Harry Kane, the England international was largely anonymous in the first-half and was roped off for Kingsley Coman, though there were concerns over his fitness before a ball had been kicked.
There was some controversy over Bayern's equaliser, which happened around a minute after Daizen Maeda had gone down with what appeared to be a head injury on the other side of the pitch.
By the letter of the law, the game must be halted when there is any head injury.
Nevertheless, Celtic captain Callum McGregor refused to blame the officials over their Champions League departure as he admitted his grief over the result.
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Celtic were left heartbroken by their late exit from the Champions League
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The Scotsman told Amazon Prime Sport: “Probably one of the cruellest [results in a Celtic jersey], the performance of the players, they gave about everything and pushed a really good Bayern side all of the way.
“Sometimes football’s cruel and you don’t get what you deserve but I have to say I’m so, so proud of the players and the way they played and handled themselves.
“We come off that pitch with no regrets. It’s a real, real sore win but I think we can be proud of ourselves.
“It was set up for us to try and nick the next one as well, and even if we had to go to extra time we fancied ourselves as well.
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Nicolas-Gerrit Kuhn had put Celtic ahead against his old club Bayern Munich
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“I think anybody watching that game of football tonight would see a really good Celtic team."
Celtic had several opportunities in the first-half after a rapid start against Bayern, that seemed to quell their noisy crowd.
Instead, the only supporters audible inside the grand stadium was the away section as Kuhn, Maeda and McGregor all spurned glorious chances.
Bayern will now face either Bayer Leverkusen or Atletico Madrid in the last-16.
