With Chelsea and Manchester City both dumped out in the fourth round, Liverpool along with Arsenal and Manchester United are heavily fancied to go all the way.
Brendan Rodgers' men travel to Crystal Palace in the fifth round on Saturday hoping to avoid a potentially season-defining result like the 3-3 draw at Selhurst Park last May that put a huge dent in Liverpool's Premier League title hopes, with City eventually crowned champions.
Palace also ran out 3-1 winners at home in the league clash between the sides in November and Carragher knows Rodgers' side can ill-afford another slip-up in south London.
"There is no doubt Palace have been a bogey team for Liverpool," wrote the legendary former Anfield defender in his weekly Daily Mail column.
"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.
"Only after that defeat were Liverpool able to start recovering and while they head into Saturday night's FA Cup fifth-round tie with an opportunity to really build some momentum, the squad will be conscious of the threat Alan Pardew’s men pose.
"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.
"They can be difficult opposition when the home crowd get behind them. This match, however, is huge for Liverpool.
"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.
"They cannot suffer at the hands of their bogeymen again."
