Liverpool's form at Anfield though has been patchy. The Reds have drawn four of the last five league matches at home and Carragher knows this has to change.
He told the club's official website: "It's vitally important we start turning these home draws into wins. Our away form is very good but we've drawn too many at home, and that's why we're a little bit behind in the league.
"The whole team has got to try to improve. Even if you think you're playing well you've got to do more, that's what football is all about.
"The other team will be looking for our weaknesses and I'm sure Fulham will think they can do something in a certain way and get something out of the game. We've all got to do a bit more and make sure we get something out of this game.
"No disrespect to Fulham, but if you have ideas of winning the league and you're playing them at home you have got to beat them.
"It's still very tight in the league. We're seventh but it's not where you are, it's the points difference. I think it's six points and we want to bridge that sooner rather than later."