The 34-year-old club legend rode to the defence of Reds boss Rodgers, who is already feeling the pressure after failing to notch up a league win in Liverpool's first four games.
"Of course he needs more time," said Carragher. "It's a long season. I'm sure Brendan will be here for a long time. He's come in and shown a lot of respect for the players. It takes time to implement his vision for the club.
"It's not as though it's his fault that we've made this kind of start. He's only bought in a couple of players. And one of them is Joe Allen, who is one of the best players around.
"He's got to be given time to stamp his authority on the club."