Eddie Nketiah’s stoppage-time penalty was only a consolation for the hosts.
Crystal Palace manager Pierre Sage felt his side had started well but paid for missed chances and costly mistakes before half-time.
“We started well, we created the chances to score first, but we missed them,” he said. “And by doing this mistake in possession and conceding the transition and set-pieces just before half-time, it was really hard to go in the dressing room with that.”
Sage said Liverpool’s pace made the task harder once Palace had to chase the game.
“With 1-0 for them, we opened the space because we had to come back to the score and we had to push. And we let a lot of space and with their speed they killed us in transitions,” he said.
“Today we defended well when we were in low block, but when we opened the space against this team with this speed, it was too difficult for us.”
Although he believed Palace had performed better, Sage admitted that their lack of efficiency remained a problem.
“A lot of times I’ve said ‘we deserved better today’. I think today it was the case too,” he said. “But football is not about what you deserve. It's about how efficient you are and we have a lack of efficiency offensively and defensively.”
Liverpool head coach Andoni Iraola was pleased to end the week with a victory, particularly after a demanding European trip.
“We needed this win, definitely, especially after the defeat the other day in Turkiye. We arrived also very late on Thursday night and an away game, another away game, and you need to find ways to win in these kind of stadiums,” he said.
Iraola felt goalkeeper Alisson Becker’s first-half save was crucial, while Mac Allister’s opener gave Liverpool an important advantage.
“In the first half the game was quite open, chances for both teams, and I think there is a save from Alisson that is key for us. And to score that first goal I think has been important,” he said.
He added that Liverpool defended with greater control after the interval and praised Isak’s contribution to Wirtz’s goal.
“The one I appreciate more is the movement he does in Florian's goal. He attacks very well the first post, he leaves the space in behind for Florian to arrive,” Iraola said.
The manager was nevertheless frustrated to concede late and lose the clean sheet, but said the win would help Liverpool prepare for their next match against Manchester United.