With three games remaining, the Reds can now look forward to a Merseyside derby at Anfield next Sunday, where a win would close the gap on neighbours Everton to two points.
"It was a great performance, we'll enjoy it and move on - we've got a great game coming up at the weekend against Everton," said Rodgers.
"We need to keep pushing and keep progressing. There are still elements of our game that we can improve. Even today we could have been better.
"The players really want to improve and learn and that bodes well for us. We knew that we had to be at our best because they needed a win. I think you could see the concentration and the character of the players. It was different class."