The Uruguayan was sitting out his first game after biting Branislav Ivanovic, but his presence was not missed as Liverpool racked up a heavy win thanks to two goals from Daniel Sturridge, two from Jordan Henderson and further strikes from Daniel Agger and Fabio Borini.
After a win that set Liverpool up in perfect fashion for next week's Merseyside derby, Rodgers said he hoped the club could now move on from the furore of the past seven days.
"Of course last week was difficult,'' Rodgers told ESPN. "I spent a lot of time talking to Luis. We move on from that, we don't want to keep bringing it up. He is suspended for 10 games. My plan is to keep him fit and working and there is a plan. It was a real test for us today.
"We do it (move forward) collectively. Luis has been brilliant, we can only move forward with the players we have. As you have seen today our focus and job at hand was fantastic.''
Liverpool dominated from start to finish and Agger's third-minute header set the tone for the rest of the game. "It was a terrific start, we were very aggressive, the pressing was very good,'' he said.
"Daniel Sturridge can prove to be one of the top strikers in Europe in the next three years, he needs an opportunity. You can see his strength, his speed, his power and his finishing as well.''
Newcastle's relegation worries deepened as they were subjected to their heaviest home defeat since 1925. They have now conceded 66 goals this season, more than anyone else, and sank to the same goal difference as Wigan.
It marked the second successive home defeat after Sunderland won 3-0 at St James' Park in the Tyne Wear derby.
"It was an awful performance by us,'' Pardew said. "We have to do something about that for next week. We have to stick together now we have to get ourselves disciplined we got run ragged today.
"I thought that (lack of experience) was evident today. Luckily we have three games to go to put it right. We need four points to make sure we are safe. They were very good today.
"They had a great energy, but there is no excuse for our performance. Defensively we were very, very poor - we will have to make a couple of changes there. The only message is we will come out fighting.
"We have had two tough games at home we have got work to do, fortunately our skipper is available, we need to show that Monday morning when we show up.''