A brace from Martin Skrtel was followed by goals from Raheem Sterling and Daniel Sturridge, before Sterling struck again early in the second half.
Bouncing back from a disappointing 1-1 draw away at West Brom the weekend before, it was a performance captain Gerrard revelled in.
“That is right up there,” he told the club’s official website. “We have absolutely demolished a top team there from start to finish. I am trying to think back of a performance, especially in the first half, that I can remember in the last 15 years.
“Maybe one or two in the Champions League got close, but that was as explosive as it gets. That’s definitely in the top three performances I have been involved in.
“You are talking about a side that is top of the league with world-class players, ones who are worth £42million; Jack Wilshere, one of the country’s big hopes who we are looking to perform at a World Cup, and Santi Cazorla.”
“I think the thing after a performance like that is: can we motivate ourselves to get close to producing something similar against Fulham?” he added.
“If we do, we will do the same to Fulham. But that is the dangerous thing. We performed fantastically against Everton and then slipped up against West Brom having taken the lead. We should have seen that game out.
“You can set markers and you can have one-off games but it means nothing if you don’t continue to play well and get something from it at the end of the season.
“We aren’t going to look back at the end of the season and think ‘How good were we against Arsenal?’ if we never got the top four. We can enjoy this but we have got to move on quickly and try to get three points against Fulham.”
Fulham vs Liverpool gets underway at 8pm on Wednesday, 12th February 2014. It is not live on TV in the UK.