Celtic crashed out of the competition after twice letting a lead slip in a 4-3 home defeat by CFR Cluj.
The Hoops made a storming start to the second half to go 2-1 ahead through goals from James Forrest and Odsonne Edouard but Scott Brown's handball allowed Billel Omrani to net from the spot.
Ryan Christie soon put Celtic back in front but Omrani quickly levelled again on the rebound in the 80th minute to put the Romanians ahead on away goals.
George Tucudean then netted with the last kick of the game to seal a 5-4 aggregate win in the third qualifying round.
Elsewhere, FC Porto - who won Group D of last season's competition and beat AS Roma in the last-16 before a quarter-final exit to eventual winners Liverpool - lost at home to Krasnodar.
Having won the first leg 1-0 in Russia, Porto were set up to progress to the next stage - but a stunning 3-2 home defeat saw them exit on away goals.
Additional reporting by the Press Association.