The Reds boss and skipper each offered their praise to their talismanic forward, who netted another two goals in Saturday's win to take his tally for the season to eight
Suarez scored a goal in each half after a Fernando Amorebieta own goal and Martin Skrtel header had given the hosts breathing space at Anfield.
His double against Fulham takes Suarez's goal tally to eight in six Premier League appearances this season and leaves Liverpool second in the table behind Arsenal.
"Our appetite for the game was outstanding," Rodgers told BBC Sport.
"Luis Suarez is a star talent but his core ingredient is his work rate, which is something we're trying to have throughout the team.
"He covers and presses and is a good talisman."
Gerrard, who played a large role in the win himself by laying on up three of his side's goals, believes the focus should now switch from Suarez's chequered disciplinary past in recognition of a genuinely world-class talent.
He told BBC Sport: "I thought we were outstanding. When it works and clicks we're emphatic, and it could have been a lot more.
"Luis Suarez is in the top five players in the world.
"A lot of people like to judge him for things he's done in the past, but I judge him as a player and he's world class."