The trip to St James' Park was the first game of Suarez's suspension, which was imposed for biting Chelsea defender Branislav Ivanovic, and Liverpool made light of the striker's absence.
His replacement Daniel Sturridge scored twice on Tyneside and Rodgers is keen to look forward as the Reds try to finish the season on a positive note.
"It has been a traumatic week for the football club but we accepted that.
"Luis did wrong, he takes his punishment and we move on. And we had to move on with a performance today and I don't think we could have done any more."
Liverpool's performance demonstrated they are far from a one-man team and Rodgers praised the collective effort.
He said: "He's been an outstanding player for us, Luis, this season and I am sure will continue to be for the future.
"Other players have scored goals, he has just been a talent. It's probably because he has played so much, he hasn't missed many games, so I can see why maybe people would label us as that.
"But we are up to 67 goals now. Luis has scored a number of goals for us and been fantastic, but you see today it's very much about the collective, how we press together, how we pass together, how we go and penetrate together.
"We got six goals and maybe could have had a few more. A priority for us was a clean sheet so we are certainly no one-man team.
"We are very much a collective group and our concentration and focus today was very, very good."
January signing Philippe Coutinho drew praise for an excellent performance, while Fabio Borini marked his first appearance since February by scoring just moments after coming on as a substitute.
Rodgers added: "We were brilliant, we were so clinical. It was a terrific start for us and to get that early goal really helps and gives you confidence.
"We talked during the week about our penetration and we have some wonderful technicians, and there is a pace and youthfulness in the side.
"Coutinho can play in a couple of positions, but above all he's a master technician. He slides the ball in, lifts it over people and he was unfortunate not to get a great goal himself.
"Sturridge can prove to be one of the top strikers in Europe in the next three years. He needs opportunities, but he has pace, power and can finish. Today he was phenomenal.
"It was nice for Fabio to get a goal after coming off the bench after being out so long.
"To score six goals and keep a clean sheet, it was very important for us."