The Reds are realistically playing for a Europa League place at best as they head into Sunday's clash at Aston Villa nine points adrift of the top four in the Premier League.
Defender Jamie Carragher admitted the defeat at Southampton prior to the international break effectively ended their Champions League hopes, but Rodgers has warned his players not to let the season "peter out".
"The Southampton result was disappointing and unexpected because we were in great form and playing well," he said.
"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.
"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."