The Merseyside team went goal crazy on Tyneside as Daniel Sturridge and Jordan Henderson led the way with two goals apiece to pile the pressure on Newcastle manager Alan Pardew.
It was Liverpool's first game since Suarez had been banned for 10 games for biting Branislav Ivanovic by the English Football Association.
Rodgers, the Liverpool manager, told the BBC: "It has been a very difficult week as a group and club - it has been a real test.
"Like we said, Luis was wrong for what he did and we take the punishment and move on. It could have been very difficult for the players with a loss of concentration. It has been a great victory on the back of a difficult week."
Daniel Agger headed them in front with just five minutes gone and Henderson made it two 12 minutes later.
Sturridge then claimed a double inside six second-half minutes. Further strikes from substitute Fabio Borini, his first league goal for the club, and Henderson rubbed salt into wounds, as did the 75th-minute dismissal of Mathieu Debuchy for a second yellow card.
"As a manager you take great pride in watching your team play like that," said Rodgers. "Our concentration and focus as well as our quality was outstanding and you have to give credit to the players for that."
While Sturridge, who started in place of Suarez, took centre stage, Rodgers was thrilled with the display of Philippe Coutinho, who set up two of the goals.
Of the Brazilian, Rodgers said: "Coutinho is only going to get better. He is a very humble boy. He is learning very quickly and has quickly adapted to this country. I think he was born with a football at his feet. He has got a wonderful touch."
The defeat keeps Newcastle nervously looking over their shoulder at the relegation battle beneath them, with Pardew's men five points clear of third-bottom Wigan Athletic, but knowing the Latics have a game in hand.
A disappointed Pardew said:"It was a day that, I am afraid, that started badly and we never really recovered. There were poor goals and defensively we were not good enough today.
"We really didn't do ourselves justice, we lost a little bit of fight and a bit of heart and it turned into a terrible score line for us."
Pardew added he would not allow the team to feel sorry for themselves, and backed them to beat the drop.
"It is very important now that we get a win, or at least four or five points more to get safe," he said.
"They were very good and we were very bad. There is nothing we can do about it, we can't turn back the clock. We have to put it right and the only way to do that is 10.30am at training on Monday morning and everyone sticking together.
"We will fight to the end, hopefully that will be enough, I think it will. Perhaps we need a bit more experience on the field and I will look at that in the selection next week."
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