Liverpool enhanced their hopes of a top-four finish and moved to within just five points of their opponents, the Premier League leaders at the start of the weekend, with a scintillating display at Anfield.
Four of the home team's goals came in an electrifying opening 20 minutes and Arsenal offered little in response, with a second-half penalty from Mikel Arteta providing scant consolation.
Martin Skrtel and Raheem Sterling scored two apiece for Liverpool, while Daniel Sturridge was on target for the seventh successive game.
"We were brilliant, (it was) a wonderful performance in such a prestigious game," said Rodgers.
"Not just the result but the performance level was absolutely out of this world."
Rodgers remained coy when asked if Liverpool could yet contend for the Premier League title.
"I'm very pleased and it's another marker for us that we're getting better and improving all the time," he continued.
"We're just trying to finish as high as we possibly can. For us, this year was hopefully going to be another big step for our development.
"The players have been incredible and we just hope to continue that development and see where it takes us.
"It's a very young side, but (they have) a wonderful appetite for the game and a wonderful ability to learn.
"They want to learn; they want to progress and you can see as time goes on that idea for us to press well and pass well, and that was key for us today.
"We do a lot of work on our pressing - I always feel that if we press well we can pass well.
"These games are normally very tight games, but I feel we could have gone on and scored more.
"I was really pleased with how we managed the game. At 4-0, the crowd are so excited and were wanting us to go for the throat, but it's important we can manage the game as well and that was a really pleasing aspect."
Liverpool's manager hailed a number of individuals, but paid a particularly warm tribute to Sterling, who will hope to gain selection in England's squad for the 2014 FIFA World Cup.
"Raheem Sterling was incredible. He's just turned 19 years of age and I don't think there's a better winger in England at this moment in time. He was absolutely phenomenal," added Rodgers.
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