Liverpool won the Champions League in 2005 and reached the final last season. Now, it is struggling to reach the second stage.
The Reds have only one point after three games, drawing with FC Porto and losing at home to Marseille and at Turkish side Besiktas.
With Marseille topping the group on seven points and Porto on five, Liverpool must win its return match against Besiktas at Anfield today for a realistic chance to advance.
"Am I surprised that we are in this situation? No. In this competition if you make one mistake you can be in trouble and that has happened," Liverpool manager Benitez said.
"Because of our past achievements, if we go out now people would say it is the end of something.
"But if we lose it is not the end of the world, and if we do the right things against Besiktas and win then we have the confidence to go forward and win again - we will have momentum."
Porto hosts Marseille in Group A's other game today. If Porto wins, Liverpool could face elimination even if it beats Besiktas and wins its remaining two games.
"I am not going to drive myself crazy by thinking about the permutations - you can't do anything about the other teams until you play them," Benitez said. "But it is a time to believe."
Manchester United and Arsenal, which drew 2-2 in the Premier League on Saturday, are the only two teams with perfect records after three games.
Arsenal is at Slavia Prague and United hosts Dynamo Kiev and wins by both English teams on Wednesday would ensure a place in the next round.
The Gunners beat Slavia 7-0 in London on Oct. 23 to equal the biggest margin of victory in the competition's history.
"Our major target is not to be complacent," Arsenal manager Arsene Wenger said. "We want to qualify as quickly as possible and can achieve that at Slavia Prague." Foxsports