Brazil have already qualified following two wins in the group and Ivory Coast trail Portugal by three points and have a much inferior goal difference heading into the final round on matches on Friday.
Ivory Coast must defeat North Korea by a wide margin in Nelspruit and hope Brazil are convincing winners against Portugal in Durban to progress.
"If we win this match maybe a miracle can happen - only God knows," defender Arthur Boka told reporters on Tuesday. "We will try to win our last match and if we exit, exit with our heads held high."
In what was dubbed the "Group of Death," the West Africans always knew it would be difficult to qualify but said they never expected the mountain to be quite so high.
Gervais Kouassi said he held his head in his hands in despair during Portugal's emphatic victory over North Korea.
"Every five minutes when I saw another goal I thought - this is catastrophic and the end for us," he said.
But he and Boka said they had to believe they could still qualify.
"We must believe we can still do it." Boka said.
Boka told reporters African teams had been unlucky not to meet high expectations at this first World Cup finals to be held on African soil.
"There are teams which in the future will make an impression - we have shown in this competition at least that we know how to play football."
"We have teams who play good football but found it difficult to finish," he said, adding hope was not lost for Ghana to progress, the only team from the continent to have won a game in the competition so far.
In a violent game with Brazil which ended with 40 fouls, Boka said a collision between Kaka and Abdelkader Keita which earned the Brazilian a second yellow card was perhaps not as harsh as Keita had made out. But he said it did merit a card.
"I think the knock on Keita wasn't that violent but you have to also look at Kaka's intentions," he said. "It's a big competition and you have to be a bit stricter so for me the yellow was justified."
