They had been reduced to 10 men in the first half when Odilon Kossounou was sent off, and were heading out, trailing 1-0, when substitute Simon Adringa levelled in the 90th minute to force the extra half-hour.
Before that, they came from behind against Senegal in the last 16 before eliminating the holders on penalties, and before that they scraped out of their group as the last of the four best third-placed teams.
“We are aware that we have made a spectacular recovery, that when you look at the Mali game we survived miraculously,” Fae told reporters in Abidjan on Tuesday.
“We will garner strength from that and tell ourselves that our mindset is good. It is that mindset which allows us to pull off miracles like that, but we are not going to relax and say that because we won miraculously it means it is our destiny that we are going to win the trophy.
“The miracle against Mali did not fall out of the sky, it did not just happen like that, it happened because the players kept on fighting and believing until the end.”
Fae was put in charge following the sacking of Jean-Louis Gasset in the wake of the Ivorians’ 4-0 loss to Equatorial Guinea in their final group game, the team’s heaviest ever home loss.
Wednesday’s match will be Ivory Coast’s first at the Ebimpe Olympic Stadium since that humiliating reverse on January 22.
From the brink of a group-stage exit, they now stand one game away from a first AFCON final since they last won the trophy in 2015.
“It would be a lie to say we have nothing to lose but we have come a long way,” said Fae as he dismissed fears his team could crumble under the pressure.
“We have put in so much effort to lift our heads back above water so we are not going to give up now because of the pressure of not getting to the final,” added Fae, who played in the Ivory Coast team that lost the 2006 final on penalties to Egypt in Cairo.
Ivory Coast are without Diakite, suspended after he was sent off while celebrating his winning goal against Mali.
Serge Aurier, Christian Kouame and Odilon Kossounou are also banned.
“It is always a loss when you lose a player but the rest of the squad will fight, grit their teeth, do their job and try to take the team through to the final,” Fae said.
© Agence France-Presse
Photo: Twitter @JamalPacman