Liverpool were held to a goalless draw at Selhurst Park as Jurgen Klopp's side failed to bounce back with a victory following their midweek defeat to Real Madrid in the Champions League.
Both sides went close to breaking the deadlock, with Jean-Philippe Mateta firing against Liverpool's crossbar from close range in the first half.
The returning Diogo Jota had earlier seen a header clip the post from a tight angle.
Mohamed Salah became the third player to strike the frame of the goal with a curling effort hitting the crossbar in the second half and bouncing to safety.