The tie was level at 1-1 following the first leg but the Scottish Premiership champions fell behind on the night and aggregate six minutes into the second half as Michael Santos struck.
An Odsonne Edouard penalty looked to have sent the game to extra time but Celtic conceded two goals in the final five minutes, through Pep Biel and Dame N'Doye, to ensure it was the Danish side that progressed to the last 16.
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Last season's Champions League semi-finalists Ajax crashed out of this season's Europa League as Getafe wrapped up a 3-2 aggregate win in Amsterdam.
Getafe stretched their aggregate lead through Jaime Mata in the fifth minute and although the hosts came back to lead on the night thanks to goals from Danilo and Carel Eiting, the Spaniards held on to record a famous victory.
Inter Milan booked their place in the last 16 with a 4-1 aggregate win over Ludogorets in a match played behind closed doors at San Siro due to the coronavirus.
The hosts led 2-0 from the first leg but conceded an early away goal as Oliveira Souza struck for the visitors.
Any nerves nerves Inter had were settled by a 31st-minute Georgi Terziev own goal, though, before a bizarre header from Romelu Lukaku made it 2-1.

Romelu Lukaku of FC Internazionale celebrates after scoring the second goal of his team with teammates Victor Moses and Nicolo Barella during the UEFA Europa League round of 32 second leg match between FC Internazionale and PFC Ludogorets Razgrad at Giuse

Image credit: Getty Images

Meanwhile, all three Portuguese sides in action on Thursday night were eliminated as Benfica were held to a 3-3 draw at home by Shakhtar Donetsk to give the Ukrainian side a 5-4 aggregate win.
Earlier, Kai Havertz had scored one goal and laid on the other two as Bayer Leverkusen beat Porto 3-1 at the Estadio do Dragao to cruise into the last 16 5-2 on aggregate.
Sporting exited alongside their Portuguese rivals after losing 4-1 at Istanbul Basaksehir after extra time to go down 5-4 on aggregate. Edin Visca gave the hosts a lifeline with a late goal in normal time and then netted a penalty to take them through to the last 16.
Bundesliga side Wolfsburg made sure of their place in the next round with a 3-0 win in Malmo that secured a 5-1 aggregate victory for the Germans.
The visitors went in front four minutes before half-time through Josip Brekalo while second-half goals from Yannick Gerhardt and Joao Victor wrapped up a comfortable win.
Justin Kluivert was on the scoresheet in Belgium, meanwhile, as Roma booked their place in the last 16 with a 2-1 aggregate win over Gent.
In-form Canada striker Jonathan David levelled the tie on aggregate in the 25th minute but Kluivert struck before the half-hour mark and Roma held on to progress.
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