Carragher made his 665th Liverpool appearance in yesterday's win over Newcastle, taking him joint second with Emlyn Hughes and Ray Clemence in the Reds' all time appearances list.
"Those names - they're giants of the club. To be anywhere close is a privilege for me and the family. They are the legends of the club and I'm just pleased to be anywhere near them," said Carragher.
"I don't think I'll catch Ian Callaghan. He's probably the nicest ex-player I've met around this place and I think he deserves that record. I think he'll keep it - hopefully he does.
"I look at the young lads coming through and I know what they're going through. The two full-backs and Jay Spearing. It doesn't seem so long ago that I was in that position. It's great for them, great for the club, and hopefully they can be here as long as I've been."