Rafael Benitez's side came in for criticism after losing two of their opening three league games but responded by coming from behind to triumph 3-2 at Bolton on Saturday.
Carragher believes that result typifies the team's character and insists they are the best in the business at recovering when on the ropes.
"We have taken a bit of criticism and rightly so, because we haven't made the best of starts," said the 31-year-old, whose team picked up 22 points from losing positions last season.
"But no-one can ever write us off. Ourselves and Manchester United, not just in this league but probably anywhere in the world, are the best at coming back from deficits and winning games.
"At Bolton, the lads showed what great character we have.
"It was so important to get those three points, especially with the international break coming up."