Ismael Saibari scored twice as PSV Eindhoven hammered Rangers 5-1 on Wednesday to book their place in the draw for the group stages of the Champions League.
Luuk de Jong, Joey Veerman and a Connor Goldson own goal all contributed to a shocking night for the Scottish side who lost 7-3 on aggregate and will now take part in the Europa League.
PSV will be joined in Thursday's Champions League draw by Belgian neighbours Royal Antwerp who beat AEK Athens and FC Copenhagen who held off Polish outfit Rakow.
After last week's 2-2 draw in Glasgow, PSV quickly took charge of the second leg with Saibari forcing a fine save out of Jack Butland.
Shortly after, Saibari got on the end of a Veerman cross to power a header past the Rangers keeper and put PSV one up in the 35th minute.
Eight minutes into the second half Saibari added his second, tapping in after de Jong hooked the ball across the face of goal.
Rangers struck back through captain James Tavernier but while their fans were still celebrating de Jong scored PSV's third, Veerman's fourth and the Goldson own goal rubbing salt in Rangers' wounds.
"It's really raw and hard to take," Tavernier told TNT Sports.
"We knew how much it meant to the fans and the club, the scoreline is really disappointing.
"We conceded too many goals. The goals we conceded are poor. We're in the Europa League now, we've got to concentrate on that."
Antwerp went to Athens with a 1-0 lead from the first leg and gave themselves a cushion when Gyrano Kerk scored in the 73rd minute.
Sergio Araujo levelled in the 90th minute but Michel-Ange Balikwisha immediately scored down the other end to give the Belgians a 2-1 win on the night and a 3-1 victory over the two legs as they made the group stages for the first time.
In Copenhagen, the home side were defending their 1-0 advantage from the first leg in Poland.
Denis Vavro doubled that lead in the 35th minute and, in spite of conceding three minutes from time when Lukasz Zwolinski levelled for Rakow, the Danes hung on to draw 1-1 and progress 2-1 over the two legs.
AEK and Rakow will join Rangers in Friday's draw for the Europa League group stage.