The Reds are on their worst run since 1987, following four straight defeats.
Liverpool lost 2-1 at home to Lyon in the Champions League on Tuesday and are set to face rivals United on Sunday.
“Beating United could be just the boost we need. We always bounce back because that’s what we are about,” explained Carragher.
“We’ve got a lot of fight and character and will want to show that against United, particularly after what happened against Lyon.
“We’re going through a tough patch but we’ve been through them before and we’ll bounce back, there’s no doubt about that.
“It’s always a great game against United, and that could be what we need. If we win, it’ll give everyone a massive lift.”
