The Anfield legend believes Rodgers is the right man for the job, but this summer's signings will be key.
Rodgers is fallen under increased pressure after becoming the first Liverpool manager to go three seasons without a trophy, with an FA Cup semi-final defeat to Aston Villa on Sunday dashing his hopes for another year.
That defeat was their second semi-final loss of the season, having been beaten by Chelsea in the Capital One Cup, while they are also unlikely to finish in the Champions League qualification spots in the Premier League.
That has led to talk that the manager should be replaced at Anfield, but Carragher insists Rodgers is still the right man for the job.
"Is he the right man? I think so," he said.
“I don’t think your whole future should be determined by one game. It was difficult with the players that came in and I still don’t think many of them have bedded in yet.”
The former defender also says that the club’s summer transfer business will be vitally important to where they finish next season.
Last summer was a busy one at Anfield as the departure of Luis Suarez to Barcelona saw the club bring in a whole host of new faces, with the likes of Adam Lallana, Dejan Lovren and Lazar Markovic all arriving for big fees.
However, not many of those signings have impressed in their first season in England, with some, Mario Balotelli in particular, expected to be sold before the next campaign.
“The signings have to be right and if they are it will make a massive difference,” added Carragher.