Rangers' defensive frailties were exposed once again as they lost to Ferencvaros to all but end their hopes of Europa League progression.
Danny Röhl's side knew they needed a win in Budapest to have a realistic chance of finishing in the top 24, and Bojan Miovski gave them hope when his acrobatic opener was given after a VAR check.
But they switched off deep into first-half stoppage time, allowing Bence Otvos to pull the hosts level with a deflected shot.
Nasser Djiga gave Rangers hope with two brilliant last-ditch challenges, but it was another lapse at the back that saw Barnabas Varga head Robbie Keane's team in front with his 20th goal of the season in all competitions.
Rangers remain on one point with just two games remaining. Ferencvaros move onto 14 and look certain to qualify for the knockout stage.
Röhl has won five in seven in the Scottish Premiership since taking over from Russell Martin but has taken just one point from 12 in Europe.
The home side passed up a glorious chance in the third minute when attacker Bamidele Yusuf easily ran through the Gers defence and screwed his shot wide of the target.
The visitors settled but in the 18th minute goalkeeper Jack Butland failed to collect a high ball in a packed penalty area following a corner and Toon Raemaekers poked the ball wide from 12 yards.
The Hungarian side, playing in green and white hoops so closely associated with the Gers' Old Firm rivals Celtic, regained the upper hand but they were undone with a moment of magic.
Miovski's spectacular hitch kick from six yards, after Danilo tried to get on to a cross from Max Aarons, appeared to be from an offside position but there were huge cheers from the Gers support when VAR confirmed the goal.
Moments later, Yusuf took a clever pass from Otvos but hit the side-netting from eight yards. Just when it looked like Röhl's side would escape down the tunnel at the interval with a lead, the 27-year-old Hungary attacker swept in a cut-back from captain Ibrahim Cisse, with the ball taking a slight deflection off Djiga before speeding past Butland.
In the 50th minute, with a chasm in the Gers defence, only a terrific recovery tackle from Djiga prevented Varga getting a shot in against Butland with the Light Blues dealing with the corner.
The stretching Djiga then blocked an effort from Yusuf as Ferencvaros remained on top, but they then took the lead when Callum O'Dowda's cross from the left was headed in by Varga who was given a free header by Gers defender Emmanuel Fernandez.
In the 87th minute, Findlay Curtis had a decent shot saved by Ferencvaros keeper David Grof but there was no late siege.
Rangers head coach Danny Röhl:
"I'm very angry about our conceded goals. This is so disappointing today for me.
"I think we played a solid first half, you go ahead and this is exactly what you want away.
"Go in to half-time with a lead, then they have to open more and more, the spaces go open and then you've got the first conceded goal, then second half, we miss so many transition moments, we lose the ball.
"Then the second one, it's too easy. We have a positioning, it's a long, long, long ball. I think the ball is 40 metres in the air. If you have the right positioning, nothing happens.
"These are the parts where we are not clinical enough.
"This is now the second game in a row in this competition I see a team who is competitive, I see a team who is in the process forward, but I see a team destroy the hard-working in two or three situations.
"To take something, you have to be sharp in 90 minutes, 95 minutes, and every duel if you do it, the chances are on today to win this game."
Your Site' Alison Conroy:
European nights had been Rangers' sanctuary during recent seasons as they struggled domestically, reaching the knockout stages of UEFA's second-tier tournament five times in the last six years.
But now they have just pride to play for in their final two games in this year's competition as the challenge Röhl faces to strengthen his side in January was laid bare once again.
Injuries have been an issue with the head coach forced to rely on a makeshift central defence of Nasser Djiga and Emmanuel Fernandez, which highlights the mistakes made by his predecessor in the summer.
Defensively weak and often devoid of confidence, it is evident the German needs more leaders to cope with the demands of playing for the Ibrox side.
Rangers' next Europa League game is at home to Bulgarian side Ludogorets on January 22. Their final fixture is away to Porto on January 29.
