Rangers exited the Europa League as Maribor claimed an aggregate victory to progress to the group stages.
Nikica Jelavic, Maurice Edu and Kyle Lafferty all missed chances as the home side tried to level the tie.
But it was Maribor who got the breakthrough on the night when Dalibor Volas slotted past Allan McGregor to cancel out Rangers' away goal.
Carlos Bocanegra fired Rangers level on the night but they could not find the goal that would have forced extra-time.
The result contributed to a hugely disappointing night for Scottish clubs with Celtic and Hearts also going out of European competition.
Rangers had two early penalty claims turned down by referee Aleksandar Stavrev, with Juanma Ortiz and Dorin Goian going to ground in the Maribor box.
Volas's second-half goal gave Rangers a mountain to climb
The home side kept up the pressure and Jelavic headed just wide before Edu nodded straight into the arms of Jasmin Handovic.
Jelavic and Lafferty combined to put the latter through on goal but Handovic made a brave save before his defence mopped up.
Lafferty and Goian flashed shots wide of Handovic's goal and the concession of numerous free-kicks added to the home crowd's frustration.
Rangers were forced into a change when Lee Wallace limped off to be replaced by Ross Perry and Jelavic headed into Handovic's grasp as half-time approached.
But the hosts had one last opening before the interval when Lafferty got the break of the ball to go through but Handovic again foiled the Scottish champions.
Steven Davis played an excellent one-two with Kirk Broadfoot to find space inside the Maribor box but the midfielder elected to pass instead of shooting and the chance was quickly gone.
And Maribor punished Rangers' profligacy as a neat passing move led to Dejan Mezga playing in Volas on the edge of the box and the striker finished well from the edge of the box on 55 minutes.
Bocanegra swivelled on the ground to convert Jelavic's knock-down from a corner to finally register for Rangers 20 minutes later.
That gave the Ibrox side more impetus and Wylde drew a save from Handovic before substitute David Healy was denied at point-blank range by the keeper.
Lafferty's header was cleared off the line and some more last-gasp defending and interventions by Handovic maintained Maribor's aggregate lead to ensure a miserable night for the Scottish side.
Rangers 01 McGregor 02 Goian 04 Broadfoot Booked 12 Wallace (Perry - 39' ) 17 Ortiz Booked (Healy - 67' Booked ) 18 Bocanegra 27 Wylde 07 Edu 08 Davis 09 Jelavic 11 Lafferty Booked Substitutes 25 Alexander 32 Perry 33 Bendiksen 10 Fleck 15 Healy 28 Kerkar 35 Hutton NK Maribor 33 J Handanovic Booked 22 Potokar (Milec - 82' ) 26 Rajcevic 44 Arghus Booked 05 Filipovic 08 Mezga (Cvijanovic - 76' ) 28 Viler Booked 70 Mertelj 10 Ibraimi Booked 17 Volas 32 Beric (Tavares - 86' ) Substitutes 13 Radan 24 Trajkovski 36 Majer 06 Milec 20 Cvijanovic 90 Gabriel 09 Tavares