Two goals in each half sent the Anfield outfit two points clear at the top of the Premier League after an eighth consecutive top-flight win, although third-placed Manchester City, who are four points adrift, have two games in hand.
And Rodgers, whose side have now gone 13 league matches unbeaten, believes the club's supporters have cause for long-term optimism.
"Outstanding team performance and I thought the supporters were brilliant today," he said. "That's as good as I've heard Anfield since I've been a manager here.
"I think they're appreciating what they're seeing. They can see that they had a long winter and it's been a tough period over 20-odd years for Liverpool.
"They can see something building here, not just for now but for the future."
But the Northern Irishman insisted that he would not get ahead of himself after another big victory.
"We're very much together here as one club," he continued. "The supporters, the players, the staff, and we're getting our rewards, but we won't get carried away.
"For us, the mantra's always been to focus on the next game.
"There's lots of people dreaming about Liverpool winning the title, but for me it's installing in the players that there's a process.
"The dream is the end result. There's a process in order to get there.
"We've got 18 points to play for, but you can only take three at a time.
"There's still some great teams up there with great managers, so we understand it's going to be very difficult.
"We just control what we do, and if we can do that we'll just see where it can take us really."
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