The Reds comfortably put their neighbours to the sword in the 222nd Merseyside derby as a header from Steven Gerrard and Luis Suarez's 23rd goal of the campaign were scored either side of Daniel Sturridge's brace.
Speaking to the club's official website, Rodgers said: "I felt that once we got the goal up front we were able to close the space and we've got real quick players on the counter attack and that allowed us to break forward and look a real threat.
"You learn from every game, both as a player and a coach. And I think against Everton you could see in the response from the players that they are always learning.
"To get a 4-0 victory against a team that has only conceded 11 goals away from home shows the real quality in our performance. The first goal was a brilliant ball in by Luis and Stevie has risen strongly and it's a brilliant header to put us 1-0 up. The second one was a perfect counter attack. The third goal, Daniel has made a great run and Kolo Toure has found him with a high ball over the top and it's a sublime finish."
The win moved the Reds four points clear of the Blues in the Premier League.