With half an hour left, Glasner introduced Will Hughes, Marc Guéhi and Tyrick Mitchell as Palace attempted to salvage something.
They were given a lifeline when Antwi was dismissed for a late lunge on Hughes, leaving KuPS down to ten men.
Immediately Palace took advantage. Mitchell whipped in a delicious cross from the left-wing, met by a brave Devenny header.
Jean-Philippe Mateta and Eddie Nketiah were immediately introduced as the Eagles went for broke. Mitchell nearly turned home an effort on the spin, but the KuPS defence proved hard to break down for a third time.
Nketiah then flashed an effort over from distance, with Devenny going close to his second, but the clock appeared to have run out.
And despite an additional five minutes, Palace couldn’t find a winner, meaning we finish the league phase in 10th place with ten points from our six games.
That means a two legged play-off will be contested in February, which Palace will need to navigate to qualify for the Round of 16.
The Eagles return to action against Leeds United in the Premier League on Saturday evening (20:00 GMT).
Palace: Benítez (GK), Canvot, Lerma (Guéhi 64), King (Nketiah, 76), Benamar (Hughes 64), Rodney, Devenny, Sosa (Mitchell, 64), Drakes-Thomas, Esse, Uche (Mateta, 76).
Subs: Henderson (GK), Matthews (GK), Richards, Lacroix, Wharton, Pino, Casey.
KuPS: Kreidl (GK), Savolainen, Pennanen (Toure, 65), Parzyszek (Konate, 77), Arifi, Oksanen, Cisse, Miettinen, Antwi, Hamalainen (Ricardo, 65), Ruoppi.
Subs: Hakala (GK), Pitkänen (GK), Voutilainen, Voutilainen, Sadiku, Luyeye-Lutumba, Lötjönen, Armah, Golubickas.