Oliver Glasner's side must settle for a play-off place after the early lead established by a superb Christantus Uche strike was overhauled by goals from Piotr Parzyszek and Ibrahim Cisse.
Justin Devenny hit back in the 77th minute shortly after Clinton Antwi had been sent off for a vicious tackle on Will Hughes, but Palace could not find the winner needed to clinch a top-eight finish in the league phase table.
Glasner made 11 changes in recognition of a schedule that sees the Eagles play two matches in 48 hours with Leeds next up on Saturday.
Sixteen-year-old Joel Drakes-Thomas became their fourth youngest player to ever pull on the shirt and there were also debuts for fellow academy teenagers Dean Benamar and George King, although the bench was stacked with experience.
For a team that Glasner revealed had barely trained together, Palace looked comfortable throughout a one-sided first-half that just missed more goals.
Uche lit the way with a beautiful sixth-minute finish after a slick passing interchange down the right ended with the Nigerian forward finding the corner with a curling shot off the outside of his right foot.
The goal settled any nerves with Palace in control for the rest of the half, creating a series of half-chances against opponents who were playing out of season.
But in the second half, Otto Ruoppi charged through a non-existent Palace midfield and with Saku Savolainen supplying the final pass, Parzyszek steered a fine shot into the corner.
KuPS had been rewarded for their first meaningful attack of the game and three minutes later they took the lead when Cisse stabbed Antwi's strike into the net as the home defence failed to deal decisively with a corner.
Hughes, Marc Guehi and Tyrick Mitchell were brought on in the 63rd minute to reinforce a midfield and defence that had started waving the Finns through with Parzyszek having a second goal ruled out for offside.
KuPS suffered a setback when Antwi was shown a red card and moments late Palace equalised when Mitchell crossed to the far post for Justin Devenny to nod home.
On came Jean-Philippe Mateta and Eddie Nketiah and despite relentless late pressure, the winner proved elusive.
Mainz beat Samsunspor 2-0 to seal an automatic last-16 place along with Raków, Sparta Prague, Rayo Vallecano, Shakhtar Donetsk, AEK Larnaca, AEK Athens and already-qualified Strasbourg - thanks to two goals deep into stoppage time to go straight to the last 16 in March.
Palace, and Fiorentina, bottom of Serie A but twice Conference League runners-up, are seeds among the teams from ninth to 24th who will play off in February for a last-16 berth, with a draw to determine the exact pairings on January 16.
with DPA
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