The 2004 European champions take on the West African side in search of not only their first victory in two World Cup campaigns, but also their first goal.
Greece lost 2-0 to South Korea in their first Group B game. Their 1994 campaign ended in failure when they lost to Nigeria, Argentina and Bulgaria, conceding 10 goals and scoring none.
"The most important thing is to play the way we played in the preliminaries," said Torosidis on Tuesday.
"If we don't play like that, if we don't respond in the match, it doesn't matter if we are playing Nigeria or the worst team in the world - we have no chance."
Greece came second in their qualifying group behind Switzerland and beat Ukraine in a play-off.
A storm of criticism back home followed the loss to South Korea with one newspaper calling for the team to be brought home rather than risk further embarrassing the nation, and others urging a less defensive approach.
Powerful Greek defender Sotiris Kyrgiakos said he was ready for Nigeria after his shock omission from the opener.
The rugged defender was considered the heart and soul of the Greek defence ahead of the tournament. The pony-tailed player is attack-minded and is dangerous with headers from set pieces.
"To be honest, every player wants to play, there's no doubt about it. But the most disappointing thing for me is not that I didn't play, the most disappointing thing for me is that the team didn't win," he said on Tuesday.
"I'm ready to play, if I'm selected."
