"We knew it was going to be a big match. I'm more delighted for the players and supporters," Rodgers told the club's official website (liverpoolfc.com).
"For me, it's three points; I'll be more delighted at the end of the season if we can arrive in the top four. I'll probably over-analyse the performance and see the areas we can improve on going forward."
Tuesday's victory at Anfield was pretty close to what Rodgers has long expected of his team despite a poor penalty miss from Sturridge that would have made the score 5-0.
"We were clinical in front of goal. We scored four and could have had arguably two or three more. It was a brilliant win for us and I'm delighted for everyone," he said.
"For us, it was a tireless performance.
"To win the big games like these here, you've got to attack and defend together, and I thought our unit - right the way from the goalkeeper to the front players - worked tirelessly at filling the spaces.
"Then, when we had the ball, we looked a real threat.
EXPOSED EVERTON
"All wins are important, but especially against your rivals. We know there's still a wee bit to go but psychologically it was a big, big win for us and one that can reiterate the confidence and belief in the squad."
The victory moved Liverpool onto 46 points, six behind leaders Arsenal, and while a title challenge appears too big an ask for his emerging side, nailing down a Champions League berth that goes with a top-four finish remains an achievable target.
His counterpart Roberto Martinez felt Everton lost their composure after Gerrard had opened Liverpool's account with a 21st-minute header from a corner.
"It means a lot and once we conceded the first goal maybe we got a little bit emotional with the game and we pushed so much forward to get that equaliser that we left ourselves a little bit exposed," the Spaniard said.
"We started well enough but conceded the goal from a dead-ball situation and we put ourselves in Liverpool's hands really," Martinez added after his team dropped four points behind their Merseyside rivals.
"We lost our concentration, lost our usual shape and it was unlike us.
"We were the team with the best defensive record in the division and we have been playing in a really positive and impressive manner. It's a moment to assess the whole season as well as tonight."
(Reporting by Amlan Chakraborty; Editing by John O'Brien)
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