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.
Defender Jamie Carragher has admitted thoughts of a top-four finish "have been put to bed" by defeat at St Mary's, but Rodgers insists there is no chance of the players switching off.
"The Southampton result was disappointing and unexpected because we were in great form and playing well," he said.
"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.
"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.
"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."