With no silverware to play for and Champions League qualification a distant nine points away with eight matches remaining, the best the Reds can realistically hope for is a Europa League spot. The surprise defeat at Southampton before the international break brought the momentum of three successive league victories to a crashing halt.
But Rodgers insists there is no chance of the players switching off, and he said: "It is very important the season doesn't peter out and it can't do. We are at a stage of the season when we don't have a trophy to play for as such but we have to fight."
He added: "The Southampton result was disappointing and unexpected because we were in great form and playing well.
"It (the international break) has given us a chance to analyse and reflect on it and sometimes you have to after a performance like that when there were no positives.
"This is a club where supporters pay good money home and away to watch the club. This is a club where there is institutional pride playing for Liverpool. Of course we always want to be challenging for trophies but if that is not the case you represent the shirt and the city and every game is vital.
"Every position we can grow in the Premier League this season is important for us. We are looking to finish the season with strength and continue. It is very important we finish the season well as that can provide a really good platform for us for next season."
Even though Europa League football is by no means a certainty for Liverpool, Rodgers is confident they will still be able to attract the right players in the summer without it.
"Whether we are in Europe or not we are going to be able to attract good players here," he added. "That (Europe) is where we would like to be but if it isn't to be then I still believe we will be able to get in players who can improve us.
"That is the challenge, to bring those players in over the coming months."