The vice-captain insists it is too early to have a clear idea of realistic targets this term but concedes that a return to Champions League football is high on the agenda.
Carragher told liverpoolfc.tv: "The target the manager has set is number one and rightly so. At the start of the season you have to have that target but that can change as the season progresses. If you aren't up there competing it will change.
"If we are up there challenging in November-December then we will be heading in the right direction. But I think everyone at the club will pleased if we get in the top four this season because that's certainly where the club needs to be."