The Reds won the game 1-0 thanks to a goal from Dirk Kuyt.
Greece defender Sotirios Kyrgiakos was sent off in the first half for Liverpool.
Gerrard told Sky Sports: “That is what derbies are all about. There was passion, commitment and fight. We beat a very good Everton side today with 10-men and we should enjoy this result.
“We played some good football and had a great attitude, sticking together. We knew we would be up against it at times and if we had the chance at a set-piece we could grab a goal.”
“The ref was superb,” added Gerrard.
“He let tackles go and that’s what fans pay their money for. There were some mis-timed tackles but we can’t complain and I don’t think Everton will either.”
