A huge chance arrived just 14 minutes from time, Nketiah and Muñoz combining to tee up Pino from a few yards out. The Spainiard went for the near post but Penders reacted to save.
Strasbourg immediately won a free-kick up the other end and it proved decisive. Enciso’s clever effort came back off the crossbar, but with Henderson stranded, Samir El Mourabet reacted to tap home, his first ever senior goal.
It remained end-to-end in the closing stages, Strasbourg substitute Kendry Paez forced a brilliant save out of Henderson, who was also forced to react to keep out Moreira’s free-kick.
At the other end Pino went close again after great work from Sarr, but couldn’t keep his shot down, with the Eagles unable to create one last chance in four minutes of injury time.
The defeat leaves Palace 18th in the Conference League table, with maximum points potentially needed to secure that all-important top eight finish.
The Eagles return to European action against Shelbourne in two weeks’ time, and host Manchester United on Sunday in the Premier League.
RC Strasbourg: Penders (GK), Doué, Høgsberg (Chilwell, 43), Sarr, Barco, Doukoure, El Mourabet, Moreira, Enciso (Omobamidele, 89), Nanasi (Páez, 74), Emegha (Panichelli, 74)
Subs: Bajic (GK), Kerckaert (GK) Amougou, Godo, Amo-Ameyaw, Nzingoula, Lemarechal, Rafael Luis.
Palace: Henderson (GK), Canvot, Lacroix, Guéhi (Richards, 45), Muñoz, Hughes (Wharton, 31), Lerma (Kamada, 82), Mitchell, Pino, Sarr, Mateta (Nketiah, 62)
Subs: Benítez (GK), Matthews (GK), Clyne, Cardines, Devenny, Esse, Uche.