Gerrard underlined his enduring brilliance with a hat-trick in Tuesday's 3-0 win over arch-rivals Everton.
The 31-year-old, who memorably led the Reds to Champions League glory in 2005, has been the heartbeat of the club, and its chief inspiration, for well over a decade.
Carragher feels his performances, when set in their context, now eclipse those of some of the club's most revered players.
Carragher told the Daily Telegraph: "Because of what he has done for the club, I believe he is the best.
"[Kenny] Dalglish, [Graeme] Souness and Ian Rush all played together in a great team, but because football is a team game it's been harder for Stevie because he's not always played in great teams.
"For me, his performance in 2006 FA Cup final stands out even more than Ian Rush in the 1986 FA Cup final and he's also regularly produced it in the major events such as the 2005 Champions League final."
Gerrard was controversially overlooked for the role of England captain last month and Carragher believes that was a mistake.
He said: "I was shocked and surprised by that decision.
"Scott Parker is a great player and everyone respects him, but Steven Gerrard should be England captain.
"He was captain in the World Cup, has been one of the best players for his country for 10 years and there was no debate to be had for me."
Carragher believes only Sir Bobby Charlton, England's record goalscorer, stands above Gerrard in terms of the country's greatest midfielders.
The former England defender said: "We all know he's in the upper echelons when it comes to Liverpool players, with most having him either first or second behind Kenny Dalglish, but when you look at a list of the greats to play in English football I'd say he is second only to Bobby Charlton in terms of the best midfielders there have ever been."