The Merseyside club suffered a fourth consecutive defeat in all competitions when Crystal Palace came from behind to win 3-1 at Selhurst Park in the Premier League on Sunday.
That latest setback has left Liverpool down in 12th position following a season in which they mounted a strong challenge for the title before finishing second behind Manchester City.
Rodgers has now turned his attention to securing a much-needed victory over Bulgarian champions Ludogorets, who need a win at Vasil Levski National Stadium on Wednesday to stay in the competition.
Liverpool have lost all three Group B matches since beating Ludogorets at Anfield and face a battle to progress with leaders Real Madrid, who have won all four matches.
Both sides have only three points but know a victory would move them level with second-placed Basel, who face Liverpool at Anfield in their final group game, if the Swiss champions lose to European champions Real.
Rodgers took responsibility for the defeat to Palace, but the Northern Irishman wants his side to stand up and be counted in Sofia.
He said: "We just have to work harder. We go away bitterly disappointed with the result and the performance and we have to very quickly put it right, because we've got a massive game now in the week.
"Every game now for us, right the way through a really busy schedule, is an important game. We have to be better. We picked a team (on Sunday) that we thought could win the game, and the players who played and the ones on the sidelines are very committed.
"They give me everything every day, but at this moment in time, we're not good enough and we need to find answers very quickly.
"We've been a very close group for a couple of years, but we had to make changes in the summer. We had to bring players in - the group was very thin."
Rodgers will be hoping to welcome back Jordan Henderson after the England midfielder missed the defeat against Neil Warnock's side due to illness.
The Liverpool boss has doubts over Mario Balotelli (hamstring), Jose Enrique (knee), and Mamadou Sakho (thigh), while Daniel Sturridge (thigh), Suso (groin) and Jon Flanagan (knee) are definitely out.
Ludogorets head into the game on the back of a 1-1 draw in a top-of-the-table clash with A PFG leaders CSKA Sofia on Saturday, and know only three points will do.
A 4-0 hammering at Basel earlier this month was a major blow to their chances of reaching the last 16, having beaten Paulo Sousa's men last month.
A draw would end Georgi Dermendzhiev's side's Champions League adventure and they will be out of contention to move into the Europa League with a defeat.
Ivan Cvorovic is unavailable due to a shoulder injury.
