More to come from four-goal Suarez, says Rodgers
Liverpool's Uruguayan striker Luis Suarez shoots towards goal at Anfield in Liverpool, northwest England on December 4, 2013
The Uruguay international needed just 35 first-half minutes to smash a spectacular hat-trick in Wednesday's game, with his third goal marking his 50th Premier League strike.
He added his fourth goal with a stunning 74th-minute free-kick as Liverpool rampaged back to form.
"This is the happiest Luis has been at this club," Rodgers said.
"But there is more to come from him. He is only 26 years old, but his best years are ahead of him and those best years are going to be here. Anfield is a hand-and-glove fit for him."
Suarez took his total for the season to 13 goals and proved there is life in Liverpool's challenge for a Champions League place without his injured strike partner Daniel Sturridge.
"Luis was sheer brilliance," Rodgers added.
"It was a joy for me to watch that. I think for anyone to witness that, they would say it was a remarkable evening. It was not just the fact he scored four goals, but it was the manner of those goals.
"Luis has got to be up there as one of the best strikers in the world after that. The repertoire he showed here tonight (Wednesday) was incredible. Undoubtedly, he is a top, world-class player."
Rodgers had demanded an instant response from his side after a dismal 3-1 defeat at Hull City on Sunday and his players delivered in style at Anfield.
"That was a bit of a tap on the shoulder for us at Hull," Rodgers said. "We were only at 75 percent and you cannot afford to do that in the Premier League these days and hope to get away with it.
"But we categorically put that right against Norwich. We were up to speed and deserved everything we got. There were lots of positives for me to take away from this."
Norwich manager Chris Hughton also hailed the striking masterclass delivered by Suarez, following a defeat that left his side in 16th place.
"He is undoubtedly a world-class player and I am sure it was a joy for Liverpool fans to watch," he said.
"But I am disappointed by how much space and time we gave him. If you give a player of his quality the space we gave him, then that is what they can do. I think we could have done more to stop him."
Liverpool had looked nervy in the opening exchanges, but they settled in the 15th minute when Suarez broke the deadlock in devastating fashion.
Norwich goalkeeper John Ruddy would have been disappointed with a goal-kick that made it only as far as Martin Skrtel.
When the centre-back headed the ball straight back towards the Kop end, Suarez allowed it to bounce twice before taking it in his stride to smash a glorious 35-yard shot over Ruddy.
Suarez's second goal, on 29 minutes, saw him swivel just inside the six-yard box to dispatch a corner from Philippe Coutinho.
Anfield was positively buzzing just six minutes later when Suarez returned to his right foot to claim the hat-trick.
The striker made Leroy Fer look leaden-footed when he flicked the ball over him on the edge of the box and then drilled a low shot across the box and inside Ruddy's left-hand post.
The Uruguayan added his fourth with 16 minutes to play, stepping up to curl a 25-yard free-kick right-footed over the Norwich wall and beyond Ruddy's dive into the top-left corner.
Norwich pulled a goal back in the 83rd minute when Bradley Johnson glanced a header from a deep cross beyond helpless Liverpool goalkeeper Simon Mignolet.
Sterling had done little all evening, but he pounced for Liverpool's fifth goal from close range in the 88th-minute, with Suarez this time the provider.