The Reds veteran has also spoken of his pride after making his 665th appearance for the club in the 3-0 over Newcastle - matching the record of Ray Clemence and Emlyn Hughes
The Scot replaced Roy Hodgson with the team sat only four points clear of the relegation zone, but having seen his side beat Newcastle 3-0 at Anfield on Sunday, the Reds are now fifth, favourites to qualify for the Europa League after leapfrogging Tottenham.
Now, the former England defender has praised the Kop legend, stating that he has had a massive impact since returning to the helm after over a decade out of football management.
Speaking to the club's official website, he said: "It's difficult to put your finger on what he's done.
"He's Kenny Dalglish - he's a legend as a player and a manager. His record speaks for itself - four championships. There aren't many managers who can say that.
"He's had a massive impact on the club and we're just enjoying it."The victory over Alan Pardew's side saw Carragher make his 665th appearance for the Anfield outfit and the defender has spoken of his pride after becoming joint-second in the club's all-time appearance list, a position he shares with Ray Clemence and Emlyn Hughes.
He said: "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."
The defender is still some way off the club's leading appearance maker Ian Callaghan, who turned out for the Reds an incredible 857 times, and Carragher admitted that he is unlikely to break the midfielder's record.
He said: "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."
Carragher is set to captain Liverpool for the remaining few games of the season due to Steven Gerrard's absence through injury, and the veteran has insisted that belief is high at the club as they look to secure fifth spot in the league.
He said: "The mood is good. We had a poor result at West Brom away and we had some tough games coming up. People maybe felt the season would peter out but we're on a good run now.
"Hopefully we can take it into next season because however well we're doing now, fifth or sixth place is still not good enough for Liverpool.
"We're on a good run and we've got to keep it going and put pressure on Tottenham."