The Uruguayan international netted twice either side of half time as the Reds dominated Martin Jol's side at Anfield.
Rodgers told BBC Sport: "Our appetite for the game was outstanding. Luis Suarez is a star talent but his core ingredient is his workrate, which is something we're trying to have throughout the team.
"He covers and presses and is a good talisman. Our quality was very good. At half-time I said I wanted us to be relentless, to keep pushing. But our intensity was outstanding after the first whistle.
"We saw today as a very important game, and we made an excellent start. Home games are important, so it was a good victory for us."
Liverpool are second in the Premier League, two points behind leaders Arsenal.