The Reds stretched their winning run to four matches courtesy of Raul Meireles's 69th minute volley and the vice captain admits it was all the more pleasing given the hype in the lead up to the clash at Stamford Bridge.
"It's one of the most difficult places to come," he said.
"They've got a great side and they are the champions. It's a great result. There was a lot of speculation before the game which has hyped it up, which maybe makes it a little bit more special. But it's three points and we are on a good run now and want to keep it going."
Carragher returned from injury to help nullify the threat of ex-teammate Fernando Torres, who had a quiet afternoon on his Chelsea debut.
Indeed, much was made of how the Reds would react to facing the Spanish hot-shot but Carra insists the Liverpool team were solely focused upon the three points.
"We used to play against Robbie Fowler when he went to Leeds. It's not easy. You know Fernando is one of the best strikers in the world and I'm sure he'll prove that for Chelsea. But he's not with us now. We have to focus on our own team and do our own jobs."
The victory at the home of the reigning Barclays Premier League champions was further evidence of Liverpool's resurgence under Kenny Dalglish.
Carragher accepts the players have shown a marked improvement under the new manager and hopes to see the Kop idol handed the job on a full-time basis.
"We've obviously improved," he said.
"I have great respect for Roy (Hodgson) so I would never say that things have changed for the better and all that type of stuff.
"As a club and as players we didn't do enough to help the previous manager. Our performances weren't good enough and the manager took the brunt of it. Obviously things have improved now and I think Kenny coming in has got the supporters and everyone onside.
"It's not our decision (if Dalgish is appointed full-time) - it's up to the owners. He's a hero to me and Stevie and the results are going well. That stakes his claim and if you are asking me, then I'd love him to be the manager (permanently)."
Meanwhile, the Reds' goal hero, Meireles was delighted with his fourth strike in five matches.
He added: "It's a good moment for me but the most important thing is the team and the victory. Three points is important for us.
"We tried to do our best and play good football. Now I've scored a few goals for the club and I'm happy."