Carragher acknowledges Liverpool's league form has to improve but he has faith in Rodgers to eventually revive their fortunes.
He said: "We're all very disappointed with the points total in the league but a lot of things have gone against us, like the sending-off (of Jonjo Shelvey against Manchester United).
"The manager can't affect those type of things. We should have won a couple more games.
"But now we can see the benefit of the young lads coming into the team.
"Eventually the manager's way of working will come to fruition."