The Reds have missed out on Champions League action in recent years and finished 8th last season in the Premier League.
"The target this year is a top four finish. Itís just so important," Carragher told TalkSport. "We won a trophy and got to a final of the FA Cup but itís still not good enough.
"The owners decided to change [the manager] and that shows to everyone how important the top four is to us and the whole of football.
"That has to be the target this season. When you look at the competition in there, itís getting stronger and stronger though.
"A couple of years ago we were in it every season, there were only really four teams in the league that that could get there and now thereís six.
"Theyíre always going to be teams that are disappointed and in the last few years itís been us."