Four goals in the first 20 minutes - the first coming after just 52 seconds - left the Gunners reeling. Defender Martin Skrtel scored the first two, with forwards Raheem Sterling and Daniel Sturridge following his lead.
Sterling added his second just after half-time and although Mikel Arteta pulled one back from the penalty spot with 20 minutes to go the match was well over as a contest.
"You only need to look at our squad really, that can be an indication," said Rodgers.
"The objective has always been to finish as high as we can but you also have to look at the other teams around you. You only have to look at what Arsenal had on the bench today.
"I want to be in a position where we can really challenge for the title here and the players have been incredible - we just hope to continue with that development and see where it takes us.
"There is no doubt we have been outstanding for a big part of the season.
"We have had one or two off days but in the main our consistency and quality of our game has been incredible.
"We will keep focused and keep our concentration."
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