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. It’s just so important,” Carragher told TalkSport. “We won a trophy and got to a final of the FA Cup but it’s 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, it’s 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 there’s six.
“They’re always going to be teams that are disappointed and in the last few years it’s been us.”
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.