Carragher is desperate for Liverpool to return to the Champions League.
He told talkSPORT: "I think with us not being in the Champions League over the last few years, everyone at the club is desperate to get back in there and get those great nights back at Liverpool.
"To do that it's going to be tough but that doesn't mean we don't want to win the league, of course we want to win the league, it's been too long but I think to go from [sixth] to winning the league is maybe too much of an ask for us.
"If we start the season well and after a few months we're still up there with the top teams why not look at that situation then.
"I'm desperate for the club to get back into the Champions League and if we start well we'll take it from there."