The incident occurred during Liverpool's 2-2 draw with Chelsea on Sunday when the Uruguayan lunged at the defender following an altercation in the penalty area. Suarez later went on to score Brendan Rodgers's side's equaliser.
Carragher wrote in his column in the Daily Mail: "It was wrong on all levels. You simply don't expect to see a grown man bite another grown man — that is behaviour you would associate with nursery school.
"But the way things are now being pitched is that Liverpool have got to do something about the rotten apple in their midst.
"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."
The striker has since apologised for his attack on the Chelsea defender and has accepted a charge of violent conduct from the Football Association, but believes it doesn't merit more than a three-match ban.