Carragher believes past experiences have taught him that once a team can guarantee a regular place in the Champions League, mounting a challenge for the Premier League is a natural progression.
"We all realise now the Champions League is very important," Carragher told liverpoolfc.tv. "It's the place to be seen and we are not there. Liverpool fans probably don't want to hear it, but it is an achievement getting into the top four. It is different to what it was a long time ago.
"Let's try and get back in that top four first as quickly as we can and then once you cement your place in there, you establish yourself and go again really, as we did with Gerard Houllier and Rafael Benitez.
"We were in the Champions League for a couple of years and then had that tilt at the title and just fell short. I think at the moment the task is to try and get back into that top four."