Carragher revealed he still has sympathy for former boss Kenny Dalglish, who was sacked in May after the club could only finish 8th, but admits he sees the arrival of Rodgers as an "exciting project".
"We all look at how Swansea played last year - they were a breath of fresh air for the Premier League and I think that's probably one of the reasons why Brendan Rodgers has got the job," said the 34-year-old.
"He has a lot of experience coaching-wise - he's worked with Jose Mourinho. So we're all looking forward to it.
"Obviously we're disappointed for Kenny [Dalglish] and the staff because I got on well with them but we have to move forward and get right behind the manager."