Suarez is on Wednesday set to find out the length of the ban he will receive from the Football Association for biting Chelsea's Branislav Ivanovic at the weekend.
The Uruguayan pleaded guilty to violent conduct and could be facing a lengthy suspension but Liverpool have stood by their man and ignored some calls to show him the Anfield exit.
And Carragher cited examples - including himself, Graeme Souness, Robbie Fowler and Jan Molby - of players who Liverpool had backed to their benefit following misdemeanours.
"The way things are now being pitched is that Liverpool have got to do something about the rotten apple in their midst," he said in the Daily Mail.
"It is as if Luis is the only player to have represented Liverpool who has ever been embroiled in controversy. That simply isn't the case."
He added: "Every one of the players I mention regretted what happened and Luis is the same. More importantly, the club stood by every one of them."
Carragher also attempted to put the incident into perspective, saying it was not as bad as leg-breaking tackle.
"The bite was shocking, no question, and everyone who has seen it was amazed," he said. "Yet was it worse than a challenge that could end someone's career?
"I know what it is like to have your leg broken by a reckless tackle. Lucas Neill cost me six months of my career in September 2003 when he played for Blackburn. Would I have preferred to have been bitten? Absolutely.
"I suspect that Branislav Ivanovic, who has conducted himself with great credit in the aftermath, would agree."