Adam Idah scored twice in the space of three minutes for Celtic but the Scottish champions fell short against Aston Villa, who booked their direct passage into the last-16 of the Champions League with a 4-2 win at Villa Park.
Morgan Rogers was the Villa hero, scoring a treble in front of the watching England manager Thomas Tuchel to earn victory which sealed an impressive debut Champions League league phase for Unai Emery's men, who finished eighth out of 36 teams.
For Celtic, the defeat means they finished 21st in the league phase meaning they will play either Real Madrid or Bayern Munich in the play-off round, the draw for which is made on Friday.
Villa needed to win and hope other results went their way to avoid a play-off round and they looked like they would hold up their end of the deal with ease as Rogers scored twice in the opening five minutes.
But Republic of Ireland international Idah slammed in two goals in the run-in to half-time to leave the visitors level at the break, taking his tally of goals in Europe this season to three overall.
The first was a brilliant improvisational finish, Idah reacting quickly after Greg Taylor's fizzing low cross was inadvertently diverted into his path by a sliding John McGinn. The Ireland striker managed to contort his body and slam home a volley from close range.
Two minutes later, he found the equaliser, side-footing home from Reo Hatate's cross from the right.
Startled, Villa composed themselves and regained the initiative, Ollie Watkins restoring their lead after Celtic were exposed on the counter-attack.
Watkins has been the subject of a rejected bid from Arsenal, reported to be £60m, with news breaking just hours before the final European league game at Villa Park.
The 29-year-old put the distraction aside as he scored in an eventful game, which also saw him miss a penalty.
Tellingly, he celebrated his goal by tapping the badge and looks certain to remain a Villa player after the transfer window closes on Monday.
Watkins should have added a second from the penalty spot but slipped as he went to take, the ball spooning embarrassingly high and wide.
But it was of little consequence with Villa seeing out the win, Rogers sealing his hat-trick at the death.
