AEK Athens 2 - 1 Celtic (agg 3-2): Hoops out of Champions League
Brendan Rodgers, who had taken the Hoops to the group stages of the competition in his first two years in charge, had admitted the third qualifying round tie in the Olympic Stadium was his biggest qualifying challenge to date following the 1-1 draw in the first leg at Parkhead last week.
Within six minutes his side were trailing to a Rodrigo Galo strike and it looked a forlorn task for the visitors when Croatian striker Marko Livaja headed in a second five minutes after the break.
Parkhead substitute Scott Sinclair pulled a goal back in the 78th minute but despite a grand finale the Scottish champions could not fashion a second which would have put them through on away goals.
Dropping down to the Europa League, where they will play Latvian side Spartaks Jurmala or Lithuanian side Suduva, is a huge blow for Celtic who will miss out on the prestige - not to mention the vast sums of money - to be earned in the Champions League.
There were ominous signs for Celtic beforehand.
Pre-match speculation about the fitness of Odsonne Edouard proved well-founded as the French striker and record signing missed out with a knock, with Leigh Griffiths keeping his place.
Fit-again striker Moussa Dembele returned to the bench, however, but with Kristoffer Ajer suspended and fellow defender Dedryck Boyata missing through injury amid speculation about his future, Rodgers paired Jozo Simunovic with Jack Hendry in central defence.
The 70,000-capacity stadium was only around half-full but the home fans roared when Niklas Hult, at the second attempt, got his cross pass fellow Swedish defender Mikael Lustig to Brazilian midfielder Galo, who swept it past keeper Craig Gordon from 12 yards.
It was the start the Parkhead side had feared and moments later they almost conceded a second when Victor Klonaridis, who scored in Glasgow last week, burst into the Hoops box but toe-poked a shot wide of the target from eight yards.
Having taken the lead, however, the Greek side simply sat back to defend it.
Celtic took control, with Tom Rogic and Griffiths both having luckless efforts on goal before the latter sent a fine Callum McGregor cross inches past the post from eight yards.
Hendry headed a Griffiths corner over the bar just before the interval but any positivity Celtic’s response elicited evaporated early in the second half when Galo’s free-kick to the back post was headed back across goal by Vassilis Lampropoulos for Livaja to head past Gordon.
Again Celtic responded positively and only a brilliant save by AEK keeper Vassilis Barkas prevented Simunovic’s header from a Kieran Tierney cross speeding in at the near post.
Rodgers brought on Dembele for Lustig in the 59th minute but Klonaridis missed a great chance to make it 3-0 when he flashed Livaja’s cut-back high over the bar.
Celtic kept piling forward and minutes after Sinclair came on for Rogic he gave the Hoops hope when he headed in a Tierney cross.
But the Greeks held out in the nervy final minutes, despite Simunovic coming agonisingly close with a flick in the last of five added minutes.