Udinese's Antonio Di Natale capitalised on a defensive blunder to secure a 1-1 draw at the Stadio Friuli and deny Celtic the away victory they needed to book a place in the knockout stages of the Europa League.
The visitors took the lead in the 29th minute when Gary Hooper took advantage of a mix-up in the Udinese defence to tap in from a yard out and Celtic looked well placed to progress from Group I as runners-up.
But veteran striker Di Natale notched from close range himself with seconds remaining in the first-half after Celtic defender Cha Du-Ri inadvertently headed into his path.
The Italians qualify alongside group winners Atletico Madrid, who finished their group campaign in style with a 3-1 win over Rennes at the Vicente Calderon thanks to goals from Radamel Falcao, Alvaro Dominguez and Arda Turan.
Tottenham Hotspur failed to reach the knockout stages of the Europa League despite beating Shamrock Rovers 4-0 in their final group game.
Spurs needed at least a five goal swing and for Rubin Kazan to lose, but the Russian side fought back from a goal down - and a man down when they had goalkeeper Sergei Ryzhikov sent off - to earn a 1-1 draw at PAOK Salonika and secure second spot in Group A, behind their Greek hosts.
Goals from Steven Pienaar, Andros Townsend, Jermain Defoe and Harry Kane gave Tottenham a comprehensive victory over Irish part-timers Shamrock, whose fans gave Spurs manager Harry Redknapp a real barracking during the match.
Despite being overwhelming favourites to top Group A when the draw was made, defeats against Rubin Kazan and PAOK with weakened sides earlier in the competition cost Tottenham dearly and Redknapp had already written off his team's chances of qualifying before kick-off.
In Greece, Rubin had Ryzhikov sent off in the 15th minute and Vieirinha scored from the penalty spot for PAOK, but Nelson Haedo Valdez levelled in the 47th minute to ensure the visitors went through.
Standard Liege players wore black armbands as a mark of respect to the three people killed by a gunman in the Belgian city this week, as the Group B winners won 1-0 in Copenhagen.
Michy Batshuayi scored the only goal in the 31st minute while Hannover, who had also already secured second place, beat Vorskla 3-1 with goals from Konstantin Rausch, Didier Konan and Artur Sobiech.
With Group C also already settled, PSV Eindhoven rounded off their group stage campaign unbeaten with late goals from Stanislav Manolev and Tim Matavz earning a 2-1 win over Rapid Bucharest, who replied through Daniel Pancu.
It was too little too late for Hapoel Tel Aviv, who beat already-qualified Legia Warsaw 2-0 in Israel. Salim Toama and Abihai Yadin won the game for the home side despite Gal Shish's second half sending-off.
Adam Maher's equaliser earned Dutch Eredivisie leaders AZ Alkmaar the point they needed to progress as runners-up from Group G after a 1-1 draw with group winners Metalist Kharkiv.
AZ knew a point would be enough barring a six-goal win for Austria Vienna, and they earned it after a frantic 37th minute in which Marko Devic put Metalist ahead only for Maher to equalise immediately.
Austria Vienna were never likely to do enough at home to Malmo but they gave themselves some hope with a 2-0 win through second-half goals from Michael Liendl and Nacer Barazite.
In Group H, Club Brugge claimed the point they needed to guarantee qualification as group winners in a 1-1 draw with Braga, who had already secured progression to the knockout stage.
Brugge, who knew defeat coupled with a win for Birmingham would see them eliminated, led through Bjorn Vleminckx's 50th-minute strike. Braga had Uwe Echiejile sent off for a professional foul after 16 minutes but nevertheless equalised in the 64th minute through Ewerton.
The result meant Birmingham missed out on a place in the last 32 despite ending their campaign with a 1-0 win over Slovenians Maribor at St Andrew's. Adam Rooney scored a 24th-minute winner for Chris Hughton's side.