Sarr, who is 22 years old, was replaced by Yves Bissouma in the 53rd minute after showing signs of discomfort in his back.
Postecoglu explained that Sarr was taken off as a precautionary measure, as the coach wasn't sure how serious the injury was.
According to Postecoglu, Sarr felt some pain in his back but didn't seem to be overly concerned about it after the game.
The coach will assess Sarr's injury further to determine the extent of the damage and how long he will be out of action.
