Dalglish has come in for criticism over Liverpool's poor league form.
“People need to remember where we were when Kenny took over again as manager,” Carragher told the Sunday Telegraph.
“The club were on their knees. We’d gone through a difficult period and found ourselves in a poor position in the league. Kenny took over and it wasn’t just that he gave everyone a lift in terms of his presence around the club, but most importantly with performances and results.
“Everyone knew this season was all about rebuilding the team and bringing a lot of new playing staff to make an improvement. Winning our first trophy in six years was a sign of that. It was a massive achievement for everyone at the club. We’re still in the FA Cup so it could get better."