After drawing with Arsenal in their first game, consecutive defeats at both Marseille and Olympiakos mean Dortmund have just one point from their first three games and a third defeat would mean they are just playing for pride.
Dortmund's main injury concern is Germany midfielder Sven Bender, who had to come off with a numb foot during his team's 1-1 draw at VfB Stuttgart in the German league on Saturday.
But Klopp says his side must match Olympiakos at home after losing 3-1 in Greece a fortnight ago as the defeat left the Germans bottom of Group F, five points adrift of second-placed Marseille and six behind leaders Arsenal.
"We need to play at least as well as we did against Stuttgart," said Klopp. "Our chances of qualifying are over if we lose. We have learned our lessons from the first three games and we know what we have to do to make this group more interesting."
While Dortmund were drawing in Stuttgart, Olympiakos were held to a 2-2
draw at home to OFI Crete and the Greeks, third in the group, need a win just
as badly as the Germans.
"It is our most important game to date," said Dortmund defender Neven Subotic. "We got ourselves into a situation where we really need a win. The faster we can score the better, because we only have three chances left to get some points."
With German cup and league games coming thick and fast for Dortmund, on top of their Champions League campaign, Dortmund face their sixth game in 19 days on Tuesday and Subotic says there is little time for anything other than resting and playing.
"All we are doing at the moment is sleeping and playing football," he said. "Sunday was a day of regeneration and lying on the couch, so to be ready for Tuesday. It's not much of a life at the moment."