After the Reds came from behind to defeat Bolton 3-2 on the weekend, Carragher said that the boys from Anfield are the most resilient in the Premier League.
"It was a great result at Bolton," he said. "I thought the lads showed what great character we have.
"No-one can ever write us off because I think 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."
Carragher was also confident that Liverpool would bounce back from a slow start in the league.
"We have taken a bit of criticism, and rightly so to a certain extent because we haven't made the greatest of starts," said Carragher.
"It was so important to get the three points at Bolton, especially with the international break coming up.
"We don't play again until Burnley at home so everyone has gone away pleased and happy."