Danny Sturridge struck twice in the romp.
Rodgers said: "We pressed together and we passed together. We scored six goals and maybe could have had a few more but the clean-sheet was important.
"We're certainly no one-man team - we're very much a collective and the focus and concentration from the group today was very good.
"I've never thought that we rely on Luis. He's been an outstanding player for us this season and I'm sure he'll continue to be. Other players have scored goals but he has just been a talent.
"We're up to 67 goals now. I've seen progress previous to today. The players have been outstanding since I have come in."
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