Nine-man Rangers were dumped out of the Champions League by Malmo in a bad-tempered encounter in Sweden.
Nikica Jelavic's goal had levelled the tie in the 23rd minute, but red cards for Steven Whittaker and Madjid Bougherra hit Ally McCoist's side.
The Swedes were reduced to 10 men when Ferreira Ricardinho saw red, but an 80th minute goal from Jiloan Hamad put the tie out of reach.
Rangers now drop into the final round of Europa League qualifying.
Uefa sanctions meant McCoist's side were without their own supporters for the away tie in Sweden, but the Ibrox side started brightly, with Jelavic threatening in front of goal as early as the eighth minute, his run brought to an abrupt halt by Malmo keeper Dusan Melicharek.
At the other end Malmo too had early chances with Pontus Jansson blasting over the crossbar, before a dipping free-kick from Wilton Figueiredo from 22 yards out caused more of a scare, with Allan McGregor having to tip over the bar.
Rangers' task was made more difficult when Whittaker was shown a straight red card after 18 minutes when he threw the ball at Malmo midfielder Jimmy Durmaz's head during a stoppage in play.
But having lost a man, Rangers gained a goal just five minutes later, Jelavic this time connecting beautifully with Maurice Edu's cross, volleying with his right foot back across goal to level the aggregate score at 1-1.
With the tie wide open, the drama continued on and off the ball.
Lee McCulloch could have little complaint about his yellow card for a challenge on Durmaz, but the Swede escaped any kind of caution when he appeared to kick out at the Rangers midfieler while on the ground in the aftermath of that foul.
The Russian referee Vladislav Bezborodov waved away the protestations of the Rangers players on the pitch, while McCoist voiced his disapproval from the sidelines.
The controversy was to continue into the second half. The Swedish champions, seemingly buoyed by their numerical advantage, started brightly and slowly built the pressure towards the hour-mark, winning a series of corners but being unable to penetrate McGregor's goal.
With the tension building, Bougherra was the next to see red in the 66th minute, the Algerian appearing to elbow Malmo's Dardan Rexhepi on the back of the head when the two players went up for a high ball.
Reduced in number yet again, Rangers tried to hold on for extra time, but to no avail.
With 10 minutes remaining, Hamad secured a place in the final qualifying round for the Swedes, striking a controlled left-footed volley from distance which caught McGregor - who had an otherwise faultless performance - off-guard.
There were chances for Rangers in the dying minutes, including an opportunity for Steven Naismith in the final seconds which he sent over the bar, but the Swedes held on to their advantage, leaving the Scots to await their fate in the draw for Europa League fourth round play-offs.