The victory propelled Brendan Rodgers' team into 10th place and continued a strong run which has seen them lose only once in their last 11 matches.
Everton currently occupy fourth spot and lie four points ahead of their Merseyside rivals, but Gerrard hopes Liverpool can further close the gap before the year is out.
"I'm really pleased with the lads. It was a fantastic performance," he told the Liverpool Echo after the win over Sam Allardyce's side.
"I think before the game people were doubting us and thinking we would be a bit toothless in the final third without our top striker. But we've gone away from home, scored three goals and got the three points we came here for.
"We're building slowly towards where we want to be. We've got two home games now against Aston Villa and Fulham. If we can capitalise and make it 12 points out of 12 then we will find ourselves a lot closer to fourth.
|TOP FOUR REDS?
|5/1||Liverpool are 5/1 to finish in the top four with bet365|
Gerrard also praised right-back Glen Johnson, who scored the first goal of the match against his former club and, according to his team-mate, ranks among the best in his position in the world on current form.
"It was a special goal from Glen and he's a player in form," Gerrard enthused. "He's been fantastic for us since the start of the season. It's no shock to me. I play for Liverpool and England with him.
"His consistency levels, and not just this season but for a long time now, have been very good. He's certainly up there with the best right-backs in the world."