Kaunas captain Radzius is mobbed after levelling the score
A header four minutes from time by Linas Pilibaitis gave Kaunas a dramatic victory over Rangers, leaving the Ibrox side out of European competition.
Kevin Thomson put Rangers ahead in the 33rd minute when he collected a Nacho Novo pass inside the box and fired past Kaunas goalkeeper Marian Kello.
But Nerijus Radzius equalised with a tremendous 30-yard free-kick just two minutes before half-time.
The killer blow for Walter Smith's side came as Rangers played for the draw.
Smith opted for just one player up front, Kenny Miller given the task of securing the vital away goal.
With Rangers' experience last season in snatching results away from home in Europe, the players showed no sign of panic in the first half.
In the 14th minute Miller latched on to a through ball and succeeded in lobbing Kello, but the ball sailed over the bar.
As in the first leg, Rafael Ledesma looked the player most likely to cause Rangers problems and that proved to be the case when Lee McCulloch picked up a booking for fouling him 30 yards out.
Ledesma's shot from the subsequent free-kick made its way around the wall but Allan McGregor was well positioned to tame it.
Rangers continued to enjoy possession in defence and midfield and were almost gifted a goal when Mindaugus Baguzis' attempt to head the ball back to his keeper missed his stranded team-mate, and the goal, by a few feet.
The stalemate was broken in the 33rd minute. Nacho Novo made a darting run down the left flank to provide a target for left-midfielder Charlie Adam.
The diminutive Spaniard fought for possession with Radzius and intelligently cut the ball in for Thomson to collect and despatch through Kello's legs.
It was only Thomson's second goal for the Ibrox side since his arrival from Hibs.
Thomson's goal wasn't enough to stop Rangers crashing out
Towards the end of the first half McGregor made an uncharacteristic error with a Ledesma curler into the box when he mis-judged the flight of the ball. The comeback keeper was relieved when the ball whizzed by his right-hand post.
Kaunas levelled the scores two minutes before the interval when captain Radzius thundered a magnificent free-kick from 30 yards beyond McGregor. Christian Dailly and his team-mates had paid the price for a pointless foul.
The Lithuanians, champions for eight of the last nine league campaigns, started the second half the brighter.
Marius Cinikas strode towards the Rangers box in 55 minutes and his left-foot shot beat McGregor but clipped the top of the crossbar.
Moments later McGregor had to react quickly to save a darting header from the edge of the box after Adrian Mrowiec had pushed up from defence and, unusually, David Weir had been beaten in the air.
With 15 minutes remaining, an error by Thomson on the left allowed Kaunas to sweep forward, where substitute Mindaugas Grigalevicius was seeking a gap in the Rangers rearguard.
Clever defending by Whittaker pushed the play wide and the danger was snuffed out.
Andrius Velicka came on for Adam to face his former team and he squandered Rangers' best chance of the second half when he shot over the bar.
Sasa Papac made a great run down the left wing and his low cross for Velicka deserved a shot on target at least.
Rangers were stung with four minutes left on the clock when Pilibaitis headed home from a corner, the ball squeezing past three Rangers players on its way into the net.
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