Lovren was bought from Southampton for £20 million at the end of last month, but only made his first appearance with his new club in the 4-0 win over Borussia Dortmund on Sunday.
The Croatian international was unable to join the side on their pre-season tour of America, but made up for lost time with a goal on 14 minutes, as he headed home Steven Gerrard's corner against BVB at Anfield.
The former Saints centre-back was a dominant force at the back for the Reds and was noticeably vocal throughout - a contrast from the likes of Mamadou Sakho, Martin and Daniel Agger last term, who were all criticised for their lack of communication in the Reds' defence.
Despite Liverpool plundering over 100 goals last seaosn, they shipped an alarming 50, but Rodgers feels that Lovren is the answer to the defensivle fragility that plagued their season last term, and the Northern Irishman compared his new big-money buy to legendary defender Carragher.
Carragher retired at the end of the 2012-2013 season after 737 appearances with the Anfied outfit, and Lovren is his ready-made replacement, according to Rodgers.
He told reporters: "Of the two boys that played today, Dejan was perfect - he's what we've been looking for since Jamie Carragher left. He's a very dominant centre-half.
"He'll go and attack the ball, reads the game incredibly well and you can see his leadership qualities with his talking and guidance of the back four.
"You also saw his range of pass on both sides, left foot and right foot. His pass into [Philippe] Coutinho for the first goal was wrapped in with his left foot and that creates the nick around the corner to get us the goal.
"Like he showed us last year, he is dominant in the air in the other box, attacking it. I thought he was excellent."
Rodgers has spent around £90 million this summer on the likes of Lovren, Emre Can, Rickie Lambert, Lazar Markovic, Adam Lallana and Divock Origi and Javier Manquillo.
Origi will spend the new campaign on loan with Lille, while Markovic and Lallana are likely to miss the opener against Southampton on August 17.