The Uruguayan international scored a delightful equaliser to secure the Reds a 1-1 draw with the Magpies at Anfield, and was a constant thorn in the side of the visitors' back line.
Playing in the hole between Newcastle's defence and midfield, Suarez's movement and penetrating forward runs caused Alan Pardew's side plenty of trouble - his impressive performance deserved far more than a point.
"He plays the false nine role like Messi does for Barcelona where he moves freely and others have to get in behind him to penetrate," Rodgers told Sky Sports after the game. "Suarez's goal was brilliant. He is a world-class striker."
Fabricio Coloccini was given a torrid time by Suarez and was red-carded for an 84th-minute challenge on the Liverpool striker, who has now scored seven goals in his last nine league matches.
"Seeing it again I think it was a [red card]. The intent, it was a naughty challenge," added the Anfield boss. "I don't think there was a great deal of contact there, if I am being honest, but the ball had gone.
"Once you see the replays, he deserves to go for that. People talk about diving but I have seen a lot worse going on in the game this season going unpunished.
"It was probably frustration from Fabricio Coloccini because Luis Suarez was unplayable. I thought he was outstanding."
Yohan Cabaye gave Newcastle a first-half lead against the run of play, before Suarez levelled after the break to lift Liverpool to 12th in the table, with 11 points from 10 games.
"We are disappointed we couldn't get the win because it was the very least we deserved. We had enough chances in the game to have won it but I have no complaints.
"Once we get a number of other players that can fit the profile and the model of our game, when we dominate games like that and finish the chances it will be great for us."