Greece drew Saturday's first leg 0-0 in Athens, fielding a five-man defence but showing no real threat up front.
"Tomorrow, essentially, is the second half of this process and every player must now reach their limits," Rehhagel told reporters on Tuesday. "This is not a normal match where you can come back next week and correct any mistakes.
"Everything rides on this one game and we have to come up with a special kind of fighting spirit and passion. For me it is important when the game starts that we minimise our mistakes."
Qualification for the tournament is also the missing piece in Rehhagel's 50-plus years in the game, with the German having never taken part in a World Cup as a player or coach.
"All players survived the first match well with no injuries. On Wednesday we must be flexible and ready to adapt to anything. You know there's no way I'll discuss the lineup," he said.
Failure to qualify for next year's finals in South Africa would most likely spell the end of Rehhagel's eight-year run as Greece coach.
