Celtic's hopes of reaching the Champions League group stages were ended after they crashed to a 2-1 home defeat to Hungarian champions Ferencvaros in the second qualifying round at Celtic Park.
Neil Lennon's side last reached the group stages in 2017, but they fell behind inside seven minutes on Wednesday night when David Siger's 20-yard strike found the bottom corner.
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Celtic dominated possession and deservedly levelled eight minutes into the second period when Ryan Christie's effort deflected in.
But striker Tokmac delivered the decisive blow with a cool finish beneath Vasilis Barkas to consign the Scottish champions to their worst performance in the competition since Artmedia Bratislava knocked them out in 2005.
Two seasons ago, it was AEK Athens while last campaign it was Cluj, and Celtic may now have to negotiate the third qualifying round and a play-off to reach the group stages of the Europa League.
Celtic: Barkas (6), Elhamed (6), Jullien (6), Ajer (6), Taylor (7), Brown (6), McGregor (6), Ntcham (7), Forrest (6), Christie (6), Elyounoussi (6).
Subs: Ajeti (n/a), Frimpong (n/a).
Ferencvaros: Dibusz (7), Botka (7), Kovacevic (7), Blazic (7), Civic (7), Siger (7), Kharatin (7), Somalia (7), Isael (6), Tokmac (8), Uzuni (6).
Subs: Boli (n/a), Skvarka (n/a)
Man of the match: Tokmac.
Celtic punished for lacking clinical touch
This was a good opportunity for Celtic to progress in the Champions League and this will be a bitter pill to swallow. They were without their talisman Odsonne Edouard and it showed in torrential conditions in the East End of Glasgow in the opening 45 minutes.
Having routed Icelandic champions KR Reykjavik 6-0 in the opening qualifying round, this was a huge step up in class against a side unbeaten in their last seven European games on the road.
Ferencvaros may previously played just two competitive matches this season, but Hungary's Green Eagles have just secured back-to-back titles under Sergei Rebrov - and his team were in front inside seven minutes.
Celtic were without striker Odsonne Edouard due to a thigh complaint. The hosts lined up with Ryan Christie through the middle rather than handing Patryk Klimala the chance to lead the line.
Albian Ajeti started on the bench as he looked to continue to build up his fitness.
Celtic failed to clear Isael's corner and as the ball broke kindly on the edge of the box for Siger, the midfielder moved away from Scott Brown before finding the bottom corner with an unstoppable drive.
Lennon, who surpassed his old manager Martin O'Neill's milestone by taking charge of Celtic in a European game for the 54th time, knew his side would need to be patient, having been surprised by their opponents' 3-4-3 formation. Chances duly fell their way as the opening period progressed but all from distance.
Remarkably, Celtic had 16 shots and had 69 per cent possession but only three of those attempts were on target and all were comfortable for Denes Dibusz in the Ferencvaros goal.
Mohamed Elyounoussi and Callum McGregor both saw low drives hit the side-netting while Christie's tame effort was straight into the gloves of Dibusz as an animated Lennon headed down the tunnel at the interval.
Celtic started the second period with intent, with Olivier Ntcham's inviting delivery evading everyone, but within eight minutes of the restart the Hoops were deservedly level, albeit with a slice of good fortune.
Greg Taylor and Elyounoussi were involved as the ball was set up for Christie, and his shot looped over Dibusz via a deflection off Adnan Kovacevic.
Celtic had the chance to go ahead when Hatem Abd Elhamed's centre was met by Ntcham, but his volley struck the underside of the crossbar. It was one-way traffic as Taylor's cute pass was finished well by Elyounoussi but from a fractionally offside position.
Lennon would have been delighted with the reaction from his players, but they were undone by a sucker punch in routine fashion as a long clearance surprised Elhamed, allowing Tokmac to gain a yard and finish low beyond Barkas.
Celtic brought on Albian Ajeti and still had a number of chances to force the game into extra-time as Christie's low cross from the byline just failed to pick out Elyounoussi, and when Ntcham's speculative shot trundled through to Dibusz, Celtic's game was up.
Just three days after Bayern Munich won last season's Champions League, Celtic are already out of the 2020/21 edition, with Lennon keeping his players in the home dressing room for some time after the final whistle.
What the managers said
Celtic boss Neil Lennon: "I'm devastated. It shouldn't happen. It's a poor result and we dominated the game. We had so many chances but we conceded two really poor goals. We all have to take responsibility for it. I have to take responsibility in terms of the team selection but we had more than enough chances to win the game twice over.
"For the first goal, only Browny is getting out to close the shot while the second one is an individual error which we should've dealt with comfortably.
"It was a basic mistake. We're making basic defensive mistakes and sometimes you can't legislate for that. We did the same against Copenhagen when we were on top. Hatem was in a decent position and all he had to do was deal with it but he doesn't. But in the final third we should've done better as well as we had so many chances to score.
"The players need to buckle up. They've been OK but some of their attitudes needs to be better. I'm just detecting a bit of malaise sometimes among them and they're not as good as what they think they are. We need to analyse where we went wrong and focus on the rest of the season."
Ferencvaros boss Sergei Rebrov: "We have beat one of the best teams we have faced in qualification last year and this year. They have quality players, but I think we deserved this. Most of the time we defended, but football is about scoring the goals, not about the possession of the ball."
Analysis: Lennon gambled with his selection
Sky Sports pundit Andy Walker:
The story of the game is that Lennon gambled with his team selection. Odsonne Edouard was injured and what a difference to the team he makes. He didn't play tonight and Lennon went with four midfielders as his front four. There was no recognised striker despite having Ajeti, Ismaila Soro and Patryk Klimala on the bench.
It's a massive victory for Ferencvaros as they do not compare to Celtic in terms of their budget. This is a huge disappointment to Celtic and their supporters. It is Europa League football for them, and the gamble of not playing with a striker has not paid off for them.
Celtic couldn't have asked for a better luck of the draw to get to the group stages, playing both their qualifying rounds at home. Ferencvaros were very smart, getting the early goal and then defended deeply. Celtic lacked the killer instinct inside the box and that was down to the fact they had no strikers on the pitch for around 70 minutes.
It was all a bit powder-puff around the box and these games define your season. The pressure could now be on Celtic to sell one of their players - who knows, even Edouard who is already attracting interest from some of the big clubs in England. It's such a huge blow for everyone who wanted Celtic to go through tonight.
Celtic host Motherwell in the Scottish Premiership at 3pm on Saturday. Lennon's men are now likely to enter a one-legged Europa League third qualifying round tie on September 24, although they could be one of two teams drawn to go straight through to the play-off round. The draw takes place on Tuesday.