The Reds captain believes the goalless draw against Everton is another example of his team's shortcomings against England's top clubsLiverpool captain Steven Gerrard rued his side's inability to take their chances against the Premier League's strongest teams after the 0-0 draw against Everton on Sunday.
The Merseyside rivals played out a terse stalemate at Anfield as the hosts struggled to turn their possession into clear-cut chances without top scorer Luis Suarez.
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"Everton have improved a lot," Gerrard told Sky Sports. "Although we are disappointed not to get three points - we've lacked cutting edge against the bigger sides this season.
"We limited Everton to very few chances today and since he's come back into our team I think Jamie [Carragher] has been our most consistent player.
"I wouldn't like to be in Brendan Rodgers' shoes when he's trying to pick his replacement. I think [a goal] is all we wanted at the end – especially for [Carragher] in his last derby."
Carragher, meanwhile, playing in his final Merseyside derby ahead of his retirement at the end of the season, was content with a share of the spoils despite his hopes of a fairytale last outing against the Toffees.
"It wasn't to be and I think a draw is a fair result," he said. "It was a tense derby with not many chances at either end. It was a good day, I would have liked to have won the derby but at least we didn't lose."