The ex-defender thinks his former side cannot afford to let the FA Cup evade them this season.
The Reds travel to London having narrowly beaten Bolton in a replay last time around, with a wonder strike from Philippe Coutinho sealing their progression.
However, they haven’t won at Selhurst Park in their last two visits; a 3-1 loss earlier in the season and that infamous 3-3 draw last year that ultimately saw them lose out on the title to Manchester City.
Now, the former defender turned Sky Sports pundit has warned his former club that failing to win the tournament would be unthinkable, given the number of high profile clubs that have already exited the competition.
“There is no doubt Palace have been a bogey team for Liverpool," he said.
"They shattered Brendan Rodgers' hopes of bringing the title back to Anfield and the effects of that 3-3 draw were still being felt all the way through to last November, when Liverpool folded at Selhurst Park and were beaten 3-1. “
Focus on the cup
However, Carragher says his old side must focus on the FA Cup with Champions League qualification in the balance and a tough tie against Turkish side Besiktas in the Europa League.
Liverpool beat Tottenham earlier in the week to move closer to the Champions League places, but the race for those final two spots in the top four is finely balanced, with as many as six teams all looking to secure a spot.
“With their hopes of getting into the top four still delicately balanced and a tough Europa League fixture against Besiktas looming, they cannot afford to let the FA Cup slip away,” added Carragher.
"It is the tie of the weekend, as Palace will be aiming to inflict further misery on Liverpool and dreaming of the chance to repeat their achievements of 1990 and get back to Wembley.”