Jefte was sent off harshly for Rangers before two quick Dynamo Kyiv goals ended their Champions League hopes for another season.
Cyriel Desser’s late equalizer in the first leg had given Rangers hope and both he and Ross McCausland had chances to give them an early lead in the second leg of the third qualifying round tie at Hampden Park.
Already on the order, Jefte was punished in the 50th minute with a yellow when he jumped to win a header and was shown a red card that made it a struggle for the hosts.
They held on for 30 minutes but Philippe Clement’s side eventually collapsed and substitutes Oleksandr Pikhalyonok and Nazar Voloshyn scored in quick succession to win 2-0 on the night – 3-1 on aggregate – to send Dynamo into the play-offs to face RB Salzburg.
Heartbreak at Hampden
It wasn’t a good night for Clement’s side who will see it as a missed opportunity as they enter the less prestigious and arguably less lucrative Europa League group stage.
Rangers made a quick start and the visitors initially looked uncomfortable in defence.
However, Oleksandr Shovkovskyi’s side worked their way into the game and in the ninth minute, winger Vladyslav Kabaev teed up Rangers captain James Tavernier on the left, but his cross did not find a player, to Rangers’ relief.
Rangers went slightly ahead in the 20th minute when Jefte headed Tavernier’s cross around the far post, before curling a shot from 25 yards high over the bar a minute later.
A Dessers header from Jefte’s cross was easily saved by Kyiv’s keeper Georgiy Bushchan and then, as the Rangers pressed, the ball fell to Tom Lawrence inside the box but could not sort out his feet to take the shot away.
When they attacked, Kyiv looked quick and purposeful which kept the Rangers defense on high alert.
On the Rangers counter just after the half hour mark, Dessers played in McCausland but although his shot was parried by Bushchan, Clement’s side failed to take advantage of the loose ball.
Cerny replaced McCausland at the start of the second half which gave Rangers fans reason for optimism, but it disappeared when Jefte, booked for a touchline foul on Andriy Yarmolenko after 30 minutes, was again cautioned and sent off for an aerial challenge on Oleksandr Karavaiev.
When the dust settled on what looked like a soft second yellow, and Rangers fans cranked up their voices in defiance, Karavaiev raced out of defense but screwed his shot wide.
Kyiv took advantage of the extra players and moved with the threat before the Rangers rallied, and the game swung late to end.
In the 68th minute, Dujon Sterling replaced tired midfielder Mohamed Diomande and Ben Davies took over from Ridvan Yilmaz, who was carried off the field on a stretcher after picking up a few minutes earlier.
It was another blow for the Light Blues and Dessers seemed to take umbrage with the fans after hearing groans and moans when they lost possession when not supported.
Rangers keeper Jack Butland narrowly missed a burn, but he saved Taras Mykhavko’s long-range effort.
However, in the 82nd minute, they had no chance when Pikhalyonok shot from distance without pressure from the Rangers defence.
Voloshyn then converted a cut-back from Mykola Shaparenko to seal the tie, with Butland redeeming himself at the back when saving a shot from Vladyslav Vanat, after an early error.
Boyd: hammer blow
Sky Sports Kris Boyd on Jefte sent off:
“The way he was given a second yellow card is beyond me. He jumped with his hands at his side, the Dynamo Kyiv player went to the ground and the referee bought it and gave him a yellow card.
“I know with VAR you can’t review the second yellow card, but it’s horrible.
“You have to pick yourself, but you feel Rangers can play all night and not score.
“It’s a hammer blow for Rangers. I’m not saying they’ll beat Salzburg in the next round, but £5m would be huge, can they invest in the squad to strengthen it?
“It’s a lot of money that Rangers can’t get, especially when they went to Poland last week and the performance they had.
“Also, 39,000 at Hampden. Rangers fans are not happy and rightly so. The whole situation with this stadium is back at Rangers’ expense.
“Champions League night at Ibrox, the team collapsed. There was no atmosphere at Hampden tonight.”
What’s next for Rangers?