Anything less than victory is likely to end the five-time European champions’ hopes of qualifying for the last 16 of the continent's elite club football competition.
Liverpool, runners-up in the Premier League last season, have struggled badly since the departure of star striker Luis Suarez and their season hit a new low on Sunday as they suffered a 3-1 loss away to Crystal.
This latest setback left Liverpool 18 points behind Premier League leaders Chelsea and closer to the relegation zone than the Champions League places.
"I'm not arrogant enough to think I will be in the job through anything. Any manager will tell you they have to win games," said Rodgers. "We need to find a solution quickly because this is very disappointing, and we have no one but ourselves to blame."
Ludogorets, in their first season in the Champions League, are only behind Liverpool at the bottom of Group B on goal difference, with both sides having taken three points from their opening four matches.
Arsenal will learn from United failure: Arteta
Arsenal captain Mikel Arteta insists his side will learn the lessons of their painful 2-1 loss against Manchester United when they take on German strugglers Borussia Dortmund in a crucial Champions League clash on Wednesday.
Arsene Wenger's side need a draw against Group D leaders Dortmund at the Emirates Stadium to be sure of joining the German club in the knockout stages of Europe's elite club competition.
But a defeat could leave Arsenal needing a result in their final fixture – in an extremely hostile environment at Galatasaray – to avoid being eliminated at the group stage for the first time in 15 seasons.
Dortmund have already beaten Arsenal 2-0 in the group stages this year and won 2-1 at the Emirates at the same stage last term.
"We will have to analyse what we did wrong to lose the game, but if we played 10 times like this against United, then we would win nine and draw one," said Arteta.
“We are all ready to bounce back against Dortmund and hopefully get a place in the last 16.”
Atletico eye last 16 berth
Last season’s finalists Atletico Madrid will be looking to seal their passage into the last 16 when they face Greek champions Olympiakos at the Vicente Calderon on Wednesday.
Atletico have won seven and drawn one of their last eight home Champions League games since returning to the competition for the first time in four years last season and stretched their unbeaten home run in the league to 26 games with a 3-1 win over Malaga on Saturday.
"We are going well in the league, we are where we want to be and now we have a Champions League match in our stadium and with our fans behind us,” said Atletico defender Diego Godin.
Wednesday’s fixtures
Zenit v Benfica
Anderlecht v Galatasaray
Arsenal v Dortmund
Atletico v Olympiakos
Basel v Real
Leverkusen v Monaco
Ludogorets v Liverpool
Malmo v Juventus
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