Phillip Cocu's first game in charge of the Eindhoven side ended in disappointment as his team were knocked out of the Europa League by Unai Emery's men
Leading 4-2 from the first leg, Adil Rami's header early in the second-half extended Valencia's lead, before Ola Toivonen equalised from a close range header.
PSV pressed for two more goals that would have taken them through to the next round but could not find their way past the visitors' rearguard, who had Rami sent off for a late tackle on Toivonen.
New interim coach Phillip Cocu retained the same team that lost 3-1 at NEC Breda at the weekend with Dries Mertens and Zakaria Laybad supporting Tim Matavz up front.
Backed by a boisterous crowd at a packed Philips Stadion, PSV started with plenty of purpose as they attempted to claw back the two-goal deficit.
However, they struggled to create many clear cut openings, with Matavz coming closest with a weak effort from the edge of the box that went wide of Diego Alves' goal.
Valencia, who by this point had weathered the hosts' early storm, could have then taken the lead on the night, but Jonas' swerving strike from distance was saved well by Przemyslaw Tyton.
Toivonen should have given PSV the lead half-way through the first half, but his header from Stanislav Manolev's cross was too close to Alves, who managed to make the save.
With the Spaniards looking content to defend their lead, the Eindhoven outfit had plenty of the ball but could not make it count, and they nearly paid for their wastefulness when Jordi Alba raced clear of the Dutch side's defence but his attempted chip was saved acrobatically by Tyton.
PSV's respite did not last long, however, as Los Che opened the scoring straight after the restart.
A Valencia corner was cleared only as far as Sofiane Feghouli, whose shot from the edge of the box was headed in by Rami to give the visitors a dominant 5-2 lead on aggregate.
The goal was a killer blow for PSV, who now had to score three times without conceding again to progress to the next round.
But to their credit, they did not allow their heads to drop, and they were handed a lifeline soon after as a cross from the right was flicked on by Matavz and headed in from close range by Toivonen to restore parity on the night.
Spurred on by that goal, the Dutch side looked to turn the screw and Georginio Wijnaldum should have done better from Manolev's cross as he headed well wide of the goal.
Kevin Strootman's thumping long-range effort was then saved by Alves, as the hosts laid siege to the Los Che goal.
Rami was then sent off for taking out Toivonen with a late challenge, but PSV were unable to capitalise on their extra-man advantage as the game petered out with a flurry of stoppages.
Following their European exit, PSV return to domestic action with the visit of Heerenveen on Sunday, while Valencia travel to Athletic Bilbao.