Toure has signed for the Reds on a Bosman.
Rodgers told talkSPORT: "Kolo Toure is a player I've admired since he came into the Premier League. He was a wonderful servant for Arsenal and a part of that 'Invincibles' group and did exceptionally well, and in the transformation of Manchester City, they brought him in as one of their key players.
"We're losing an absolute colossal player in Jamie Carragher, who was absolutely brilliant for me. It's very, very hard to replace that type.
"Kolo Toure will give us that experience and winning mentality. He's still very fit, very strong and will come in, offer that support and fight for his place in the team."