Rangers crashed out in disappointing style after failing to recover from the loss of an early goal against PSV.
The Light Blues' prospective new owner Craig Whyte - whose reported £33million takeover of the club is set to be confirmed next week - watched from the main stand as Jeremain Lens scored in the 13th minute which was ultimately enough to send the Dutch side in to the quarter-finals on a 1-0 aggregate scoreline.
Rangers struggled to break free from their defensive constrictions after going behind but had an encouraging spell of pressure in the second half when Maurice Edu missed a great chance, moments before a decent penalty claim was denied when PSV midfielder Atiba Hutchinson looked to have handled the ball on the line.
However, while there could be no doubting their effort a lack of quality told in the end and Rangers must now regroup ahead of Sunday's Co-operative Insurance Cup final against Celtic at Hampden.
Despite the goalless draw in Holland in the first game, the Ibrox fans did not turn up overly confident, having watched their side win only one of their last 20 games in Europe.
Light Blues manager Walter Smith returned to his favoured 5-4-1 formation with Neil Alexander replacing Allan McGregor in goal.
Young midfielder Gregg Wylde came in for El-Hadji Diouf who started on the bench and with Nikica Jelavic ineligible, Northern Ireland international Kyle Lafferty started as the lone striker.
The early stages were frantic as the slick Dutch side showed their intentions by going all out for the away goal which would change the complexion of tie.
That goal arrived when Balazs Dzsudzsak drove in to the box past Richard Foster after taking a Erik Pieters pass and cut the ball back for the unmarked Lens to slide in to the net from close range
The PSV fans, who were in position an hour before kick-off, made themselves heard against the groans of the Ibrox support who feared a long night ahead.
The visitors grew in stature, zipping the ball around as Rangers chased shadows with Lafferty an isolated figure.
With such an emphasis on defence it was difficult at times for the home side to attack with any numbers or with conviction and when they did, they looked susceptible to the counter.
The home fans alternated criticism and encouragement as the first half raged on but in the 28th minute the tie could have been effectively finished when PSV's Swedish playmaker Ola Toivonen slipped in Dzsudzsak in at the edge of the box but the Hungarian blasted high over the bar from 12 yards.
It was as close as Rangers got to the opposition goal until three minutes from the break when defender Madjid Bougherra headed a looping Steven Whittaker free-kick over the bar.
Skipper David Weir was kept inside at the break to allow Steven Naismith - recently recovered from a hamstring injury - to support Lafferty but it was Lens who almost grabbed his second when arrowed a drive from distance past Alexander's right-hand post two minutes after the restart.
Having reverted to four at the back, Rangers promised a more positive approach and moments later Wylde made a yard of space at the edge of the PSV box before sending in a decent shot which was saved by Andreas Isaksson.
Rangers had upped the tempo markedly in a bid to rattle the Dutch side and in the 55th minute another fine cross from the increasingly confident Wylde was almost put in to his own net by PSV defender Marcelo as he cleared the danger.
On the hour mark the home side were handed the best chance of the game when the ball broke to Edu eight yards from goal but the Ibrox midfielder shot's shot was blocked by Isaksson.
The miss typified the miserable night Edu was enduring but moments later there was more misery for the home fans when the home side appeared to be denied a penalty.
After Naismith had hit the bar from close range with a header, Kyle Bartley's header was saved by Isaksson before Hutchinson looked to have handled the ball on the line.
However, none of the officials, including the additional assistant behind the goal, deemed an offence had been committed.
Diouf replaced the tiring Lafferty before Alexander made a fine save from Toivonen as the visitors almost capitalised on the break.
Dzsudzsak then fired a free-kick from the edge of the box just over the bar before Bougherra headed a Wylde corner over the bar.
In the 81st minute, as Rangers ran out of steam, Dzsudzsak came closer with a driven free-kick from the edge of the box which beat Alexander only to cannon off the post and away to safety.
The game petered out but there will be no respite for the Ibrox side who must face up to Old Firm rivals Celtic on Sunday, having yet to beat them in four previous meetings this year.