The Reds moved within four points of the Barclays Premier League top four after goals from Raheem Sterling and Joe Allen saw off the struggling Magpies at Anfield.
With fading champions Manchester City now looking vulnerable in fourth, Liverpool's hopes - which took a hefty blow in back-to-back losses to Manchester United and Arsenal - could have been reignited.
Rodgers said: "The players and myself are very motivated to do the best we can. We have shown we can put results together consistently. We have important players coming back which is good news.
"But we are looking for other teams to slip up and we have to continue winning.
"There are teams above us but, as we have seen last year, there can be changes and points dropped and I think there will be changes."
Liverpool, inspired by Philippe Coutinho, started superbly with Sterling scoring after nine minutes and several other chances being created.
Newcastle rallied before the break and had a strong penalty appeal turned down but Allen made the game safe in the second half.
Rodgers said: "It was a good performance. I thought that our attacking play was very bright, we looked exciting going forward, we worked hard in the midfield.
"At times our possession could have been better but we had a real attacking intent and created chances and could have scored more goals."
