At a Standard Chartered event inside the grounds of the team's hotel, Carragher was joined by Charlie Adam for a meet and greet session with some of the bank's staff, during which both were quizzed on their predictions for the future under Dalglish.
Carragher told liverpoolfc.tv: "Kenny has had a major impact since coming in at a time when results weren't going too well for us. Since he and Steve Clarke arrived they have done a great job and hopefully we can carry that into next season.
"It's great to work with Kenny again because he is a legend of the club, not just as a player but as a manager as well. He is someone who everyone looks up to and the foreign players will be aware of him also.
"We'll have to see how the season goes but we know that the expectations are there. We're like any club in that we want to do well.
"The start of the season is the time when things can get ruined for you if you don't get good results early on so we have to focus on that first game against Sunderland, make sure we take three points and then go from there.
"It's all well and good people saying last season that Liverpool almost made Europe and moved up the table, but our standards are raised higher than that and we want to do better."