Match ends, SK Rapid Wien 1, Rangers 0.
Rangers have failed to reach the last 32 of the Europa League after Dejan Ljubicic's late winner gave Rapid Vienna victory in Austria.
Steven Gerrard's side needed a win to qualify, but instead it is their hosts who reach the knock-out stage.
As both sides found it difficult on a rutted pitch, Rangers' Connor Goldson struck the bar with a header.
Home goalkeeper Richard Strebinger saved from James Tavernier before substitute Ljubicic slid in the winner.
That secured a first win in four home games for Rapid, who finish as runners-up to Villarreal after the La Liga side beat Spartak Moscow 2-0 in Spain.
It was Rangers' second defeat in 14 Europa League games and ends a journey that began in the first round of qualifying against Shkupi in July.
Campaign peters out in game of few chances
This was a massive opportunity missed for Rangers against a distinctly average Rapid team.
Their European campaign petered out after the early promise of a point in Villarreal and the win at home against the Austrians.
Allan McGregor was a virtual spectator until he was beaten by Ljubicic's late finish. It came at a time when Rangers were throwing everything forward in search of the goal they needed.
But it was the goalkeeper's poor kick-out that gave Rapid possession and, with a rare piece of incisive passing, they cut through the visitors' back-pedalling defence, giving Ljubicic the time and space to slide the ball into the net.
Ultimately, Rangers barely troubled Strebinger in the Austrian goal other than that late Tavernier drive that forced the goalkeeper into a good diving save.
That aside, Rangers struggled to create meaningful opportunities on a dreadful playing surface.
In truth, the state of the pitch meant neither team could put together a fluent move in their search for goals.
The closest Rangers came to finding the goal they so badly needed came from Tavernier's pinpoint free kick that Goldson headed against the crossbar.
'Work in progress Rangers fall short' - analysis
The thousands of Rangers supporters who had managed to get tickets for what might have been a momentous night stood in appreciation of the players at the final whistle. The dejected men in blue had put plenty into the match but came up short.
They will reflect on a campaign that brought results they may not have anticipated at the start of the season, but also one that could have ended better.
It was a dearth of creativity that haunted them on Thursday. In Moscow, it was poor defending and an assistant's flag that denied them a fourth, potentially winning, goal. And at Ibrox, there was the late Eros Grezda chance to beat Spartak but instead was scooped over the bar.
Rangers are a work in progress - Gerrard has been quite clear about that. A European run has been enormous fun for the supporters, but the priority has to be trying to stay within touching distance of Celtic in the league and challenging for domestic silverware.
To do that, they must quickly regroup and find a better, more consistent level of form, starting against Hamilton Academical on Sunday.
- Rangers have won just one of their 10 Europa League group games since the competition was rebranded in 2009-10
- Excluding qualifiers, they have failed to win any of their previous 12 away European games (D8 L4) since a 2-0 Uefa Cup quarter-final second leg win against Sporting in April 2008
- Rapid have reached that last 32 through the group stages for the first time since 2015/16
- They have now won their first competitive game against Rangers having lost each of their previous three meetings.
- 3MüldürBooked at 42mins
- 97IvanBooked at 26minsSubstituted forSchobesbergerat 62'minutes
- 15MarticBooked at 50minsSubstituted forLjubicicat 78'minutes
- 10MurgSubstituted forKnasmüllnerat 45'minutes
- 6GoldsonBooked at 60mins
- 8JackBooked at 43minsSubstituted forLaffertyat 79'minutes
- 23CoulibalySubstituted forGrezdaat 71'minutes
- Paolo Silvio Mazzoleni
- Shots on Target
Second Half ends, SK Rapid Wien 1, Rangers 0.
Scott Arfield (Rangers) wins a free kick in the attacking half.
Foul by Stefan Schwab (SK Rapid Wien).
Hand ball by Boli Bolingoli-Mbombo (SK Rapid Wien).
Attempt saved. Mert Müldür (SK Rapid Wien) right footed shot from outside the box is saved in the centre of the goal. Assisted by Boli Bolingoli-Mbombo.
Corner, SK Rapid Wien. Conceded by Ross McCrorie.
Goal! SK Rapid Wien 1, Rangers 0. Dejan Ljubicic (SK Rapid Wien) right footed shot from the centre of the box to the bottom left corner. Assisted by Christoph Knasmüllner with a through ball.
Attempt saved. James Tavernier (Rangers) right footed shot from outside the box is saved in the bottom left corner. Assisted by Scott Arfield.
Substitution, Rangers. Kyle Lafferty replaces Ryan Jack.
Attempt missed. Stefan Schwab (SK Rapid Wien) left footed shot from outside the box is just a bit too high from a direct free kick.
Substitution, SK Rapid Wien. Dejan Ljubicic replaces Manuel Martic.
Foul by Ryan Jack (Rangers).
Philipp Schobesberger (SK Rapid Wien) wins a free kick on the right wing.
Foul by Scott Arfield (Rangers).
Manuel Martic (SK Rapid Wien) wins a free kick in the defensive half.
Corner, SK Rapid Wien. Conceded by Gareth McAuley.
Substitution, Rangers. Eros Grezda replaces Lassana Coulibaly.
Attempt missed. Glenn Middleton (Rangers) right footed shot from outside the box is high and wide to the right following a corner.
Corner, Rangers. Conceded by Boli Bolingoli-Mbombo.