Jamie Carragher believes Steven Gerrard's performance in Tuesday’s 3-0 Merseyside derby victory firmly underlined his credentials for the title of Liverpool's greatest ever player.

The Reds captain fired an historic hat-trick against the Blues to add to an ever-growing list of accomplishments and milestones he's achieved over the course of 576 games for the club so far.

"Because of what he has done for the club, I believe he is the best," said Carragher. "Dalglish, 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.

"In their era, the First Division was full of the best players in Britain, but now the Premier League has many of the best players in the world. I definitely think it's a case with Stevie that people will not fully realise how good he has been until he stops playing.

"It's been harder for him in many ways because when you spend an entire career at one club, the supporters see you as a youngster, remember all the mistakes you've made growing up and then when you get towards the end start to ask if you're the same player anymore. Even the great Liverpool players didn't have that because they didn't join until later or left before they were finished.

"I know how hard it can be for a local lad to live up to expectations, especially for Stevie who has had so much responsibility for so long.

"None of the players who've played alongside him would dispute he's the best the club has ever had, and I would hope none of the managers would, either."

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Carragher added: "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.

"You'd put Charlton No.1 not only for his achievements with Manchester United, but because of the World Cup in 1966. Beyond that you'd have Graeme Souness, Alan Ball, Dave Mackay, Paul Scholes, Roy Keane, Glenn Hoddle, Gazza, Frank Lampard and Bryan Robson. For me, Stevie has eclipsed all of those for what he has done for Liverpool and England."

Meanwhile, Carragher believes Gerrard should be handed the England captaincy on a permanent basis ahead of this summer's Euro 2012 finals.

The Liverpool midfielder was overlooked in favour of Tottenham's Scott Parker by coach Stuart Pearce for the recent international friendly with Holland.

Carragher said: "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."