Tyrick Mitchell steered Palace into the lead and Ismaila Sarr nearly added a second when he struck the inside of the post with Strasbourg goalkeeper Mike Penders well out of his area.
Emanuel Emegha equalised for the French club early in the second half as he tapped in at the back post from Diego Moreira’s cross.
Adam Wharton hit the bar for Palace with the goal gaping as Penders was again caught badly out of position when Strasbourg lost the ball on the edge of their own box.
Penders then produced a terrific save to deny Yeremy Pino and Strasbourg went down the other end and scored as teenager Samir El Mourabet swept in the rebound after Julio Enciso’s free-kick smacked back off the post.
Palace boss Oliver Glasner said his team paid the price for not taking their chances.
“When you twice have an empty goal in front of you and you miss the goal twice hitting the post, you should be 3-1 up. Then we have the big chance against the keeper and then in the next action we are 2-1 down,” Glasner said.
“It has happened too many times this season when we did not decide the game when we could.”
Strasbourg moved level on 10 points with Samsunspor at the top after the Turkish side could only manage a 2-2 draw away to Breidablik of Iceland.
Palace are 18th in the league standings with two wins and two losses through four matches in their first full venture into European football.
They are two points off the top eight, which offers direct qualification to the last 16. Palace have games still to come against Irish outfit Shelbourne and Finland’s KuPS.
Aberdeen remain winless after a 1-1 draw at home to Armenia’s Noah. (AFP)
