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.
|PREMIER LEAGUE LATEST
|7/1||Liverpool are 7/1 with Bet365 to finish in the Premier League top six this season
"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."