With fourth-placed City reeling after defeat by Manchester United continued a torrid run in which the champions have lost six of their last eight games, Liverpool needed a win over Newcastle to retain hope of a Champions League spot.
Liverpool fans would have been excused for feeling a little jittery after back-to-back league defeats, but Raheem Sterling set Rodgers's side on their way before Joe Allen scored a late second to close the gap on struggling City with six games left.
“We are going to fight till the very end,” Rodgers told reporters.
“There is always a price when you lose big games. We are a group that's learning. We knew we had to respond to those defeats.
“I still think there will be changes and points dropped. The players are very motivated and we've shown we can put wins together.
“I thought we showed attacking intent in the game, won the ball back quickly and controlled the game until the last five six minutes in the first half, when we started to give the ball away too cheaply.”
If Liverpool are to qualify for the Champions League then Rodgers hopes his attacking duo of Philippe Coutinho and England international Sterling can continue to torment defences.
“I think Philippe Coutinho was incredible, sensational,” Rodgers said.
“He played in that hole between the midfield and their defence and was outstanding. He showed why he is one of the best players in the best league in the world.
“He is very valuable. He is a kid who's non-stop, he wants to learn and improve himself. I thought he was outstanding tonight. Wonderful skill and ability for his goal.” – Reuters
Original source: Reds will fight to the end - Rodgers