Twelve months on from eliminating PSV at the same stage of qualifying, the Gers were unable to come out on top over two legs this time around as they followed up last week's 2-2 first-leg draw at Ibrox with a heavy 5-1 second-leg defeat at the Philips Stadion on Wednesday night.
A brace from Ismael Saibari, strikes from Luuk De Jong and Joey Veerman, as well an own goal from Connor Goldson helped PSV get their revenge over Rangers, whose solitary second-leg goal from captain James Tavernier proved inconsequential in the Netherlands.
Michael Beale's side will now enter the Europa League group stage, while Peter Bosz's men will discover their Champions League group-stage opponents on Thursday evening.
Rangers made a bright start to proceedings at the Philips Stadion, but PSV grew into the game and there were plenty of warning signs of the host's threat in the final third during the first half, with De Jong missing a few close-range headers and Saibari a constant dangerman in an around the Gers' penalty box.
As temperatures began to rise on the pitch with a few heated exchanges, particularly between Todd Cantwell and Sergino Dest, Rangers' striker Cyriel Dessers drilled the visitors' best chance of the first half narrowly wide after receiving a ball from over the top.
Jack Butland then made a huge save with his left leg to keep out a side-footed strike from Saibari inside the penalty area, but the Gers goalkeeper was unable to prevent the PSV attacker from heading home the opener just a few minutes later.
Veerman ran into the left channel behind Tavernier before floating a delivery towards Saibari, who managed to get in front on John Souttar and nod the ball past Butland inside the six-yard box.
PSV successfully carried their impressive attacking display into the second half, and they were rewarded with a second goal on the 53-minute mark when Jordan Teze expertly picked out De Jong at the far post before the Dutchman hooked a first-time cross across goal for Saibari to side-foot a volley into the net from just a few yards out.
Beale turned to his bench on the hour mark with Danilo and Sam Lammers brought on, and the latter did not take long to make his mark as he set up Tavernier to provide the Gers with a lifeline in the 63rd minute, rolling the ball across the six-yard area for Tavernier to slide the ball in at the back post.
However, PSV quickly restored their two-goal cushion just two minutes later when De Jong towered above the Gers backline to glance a header under Butland's leg after meeting an inviting cross from Veerman.
Veerman then got his name on the scoresheet when he rifled the ball into the far corner from the right side of the box 12 minutes from time, before Rangers' night went from bad to worse three minutes later when a mix-up at the back led to Goldson rolling a heavy back-pass into his own net.
Rangers will now endeavour to put aside their disappointment when they play host to Old Firm rivals Celtic in the Scottish Premiership on Sunday, while PSV travel to RKC Waalwijk in their next Eredivisie fixture on Saturday.