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."
Greece, European champions in 2004, are aiming to reach the World Cup for the second time after playing in the 1994 finals.
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.
The 71-year-old is under pressure to adopt a more attacking stance, after Greek media questioned his decision to field five at the back on Saturday but he declined to reveal any details.
"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.
Midfielder Giorgos Karagounis and defender Sotiris Kyrgiakos, who missed training on Monday with minor injuries, were back on the pitch on Tuesday at the newly-built Donbas Arena. Defender Avraam Papadopoulos was also declared fit.
