The defender is talking in light of his comments about Mesut Ozil being compared to Dennis Bergkamp.
The Uruguayan was the star man at Anfield under Brendan Rodgers for several seasons, with one scintillating campaign in 2013/14 pushing them close to the title.
They were eventually beaten to it by Manchester City, with that failure to win the title ultimately seeing him leave for a big money move to Barcelona.
That title failure still haunts Liverpool, and Carragher says that not winning a trophy means Suarez won’t be remembered as much as other Anfield legends.
“Suarez at LFC is one of the best we've ever seen but won't be remembered as much as Dalglish, Rush, Barnes & SG [Steven Gerard]. No big trophies,” he wrote on Twitter.
Carragher’s latest remarks come in light of his recent comments about Mesut Ozil being compared to Dennis Bergkamp at Arsenal.
He recently wrote in his Daily Mail column that Ozil needs to win a title with the Gunners before he can be compared to the Dutch legend, and it is a similar situation with Suarez’s legacy.
Ultimately, statistics fall by the wayside when it comes remembering players, with those who produced moments of magic and won things the most remembered by fans.
And while Ozil and Suarez have produced magic at Arsenal and Liverpool, neither have managed to pick up titles, although Ozil has a chance this season, and that leaves them behind those that did at present.