The Reds thrashed Norwich City 5-0 at Anfield on Saturday, with Jordan Henderson, Luis Suarez, Daniel Sturridge and skipper Steven Gerrard all getting their names on the scoresheet before Canaries defender Ryan Bennett put the ball in his own net.
Rodgers admits that he started Carragher in order to add communication, leadership and experience to his side.
"Jamie Carragher hasn't put a foot wrong for me since I came, he has been absolutely brilliant," said Rodgers. "He hasn't played as often as he'd have liked. He's played in a lot of the cup games and I'd hoped to not put a curse on him, but I said to him that I couldn't remember him making a mistake in any of the games since I've been here.
"I thought about his leadership. We are a quiet team and he's a great organiser - he manages the game very well, he's got big experience, and he can play football.
"I thought him coming in would give us that extra bit of leadership. We saw that from him, he was fantastic."
Liverpool travel to Oldham Athletic in the FA Cup on Sunday.