A run of three games without a win in the competition meant Luciano Spalletti's side went into Tuesday's encounter needing to better Tottenham's result against Barcelona, and Mauro Icardi's 73rd-minute header looked to have booked Inter's place in the last 16.
Icardi's effort cancelled out Hirving Lozano's opener after 13 minutes, but it proved insufficient after Lucas Moura earned Tottenham a late 1-1 draw at Camp Nou.
Lautaro Martinez could have salvaged progression for Inter but he headed over unmarked from six yards out in stoppage time as the Nerazzurri slipped into the Europa League.
Icardi started brightly on his 200th appearance for the club and six minutes in he supplied a cross for Perisic, whose powerful header clattered off the upright, with Jeroen Zoet possibly getting a touch.
But Inter were dealt a blow when, having robbed Kwadwo Asamoah of possession, Steven Bergwijn crossed for Lozano and he expertly found the bottom-left corner.
Another Asamoah error almost cost Inter again two minutes later, but Samir Handanovic was out swiftly to deny Luuk de Jong.
Icardi looked set to restore parity after the restart, only for Zoet to lunge to his left and tip the striker's venomous effort wide.
Inter's captain was not to be denied in the 73rd minute, however, as he headed home from Matteo Politano's floated cross.
With news of Tottenham's equaliser spreading around San Siro the hosts rallied, but Martinez squandered the chance to make himself a hero when he failed to keep his header down, ensuring Inter's Champions League campaign came to an end.
What does it mean? Inter's Champions League return cut short
Inter's six-year wait for Champions League football looked to have been worth the wait when they picked up two wins from their first two fixtures, but they were unable to build on the strong start and added just two more points. It means the Europa League awaits, while PSV exit this season's competition without a win to their name.
Lozano, Bergwijn rampant
With Inter pushing high from the off, there was plenty of space for PSV's wingers to exploit, and it was no surprise to see them combine when Lozano headed in.
Asamoah's blunder proves decisive
He has been a consistent performer since his arrival from Juventus, but Asamoah was to blame for PSV's winner when he gifted Bergwijn possession. His mistake proved costly as Inter struggled to get back into the game.
Key Opta Facts
- Inter have failed to progress from the group stage for just the second time in their previous 12 Champions League campaigns (also 2003-04).
- PSV failed to keep a single clean sheet in a Champions League season for the first time since 1999-00.
- Bergwijn (eight goals, eight assists) has now been directly involved in 16 goals for PSV in all competitions this season, one more than in the whole of 2017-18 (15).