Gerrard stepped down from the international game on Monday after amassing 114 caps and leading England into three major tournaments as captain.
The 34-year-old cited Liverpool's involvement in the UEFA Champions League as a key factor behind his decision, having excelled on Merseyside last season when the club had no continental commitments.
And Carragher, who retired from the game a year ago, believes Gerrard will be able to give Liverpool two or three more years of sterling service after departing the international arena.
He told Sky Sports News: "For Liverpool football club, it's a great decision. I am sure the Liverpool supporters will be happy.
"You get a fresher Steven Gerrard. He had a great season last season with the demands of England.
"But there will be more demands on Liverpool this season, more expected because of the season they had last year, and Steven Gerrard is still a vital part of Liverpool - and I think he will be for the next two or three years, so for Brendan Rodgers, it's a great decision by Stevie."
Despite Gerrard's decision to step away, Carragher believes his former colleague could have continued for England, and predicts national boss Roy Hodgson will have a tough time replacing the former skipper.
"I think he could have [continued]," Carragher added.
"I think he has shown that throughout his career, he has been able to deal with the demands of Liverpool and England.
"I think just that fact of Liverpool being back into Europe now, that adds to the schedule of games.
"At times, you are playing two or three times a week because he is still vitally important to Liverpool, and I think he is also for England in some ways because there isn't a natural person you could see taking the role he has now with England in terms of that holding role, that sitting role.
"There are not many young players coming through in that role, but England will have to find someone to fill that role."
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