The 2023 AFCON hosts have been on the brink of exiting the tournament multiple times, including after a 4-0 defeat to Equatorial Guinea to end their group stage before late comebacks to beat both Senegal and Mali in the knockouts.
However, they are favourites to reach the final when they face DR Congo in the semi-finals in Abidjan on Wednesday.
But interim coach Fae, who was installed after Jean-Louis Gasset was sacked following that Equatorial Guinea humiliation, is insistent that Ivory Coast's travails could yet be for nothing.
"We are aware that we have made a spectacular recovery, that when you look at the Mali game we survived miraculously," Fae said in a pre-match press conference.
"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."
Morocco's group-stage win over Zambia two days after Fae's surprise appointment kept Ivory Coast in the competition as the worst of the four third-placed teams to qualify for the knockouts - and they have continued to ride their luck ever since.
"It would be a lie to say we have nothing to lose but we have come a long way," Fae added.
"We have come from very far, we have made every effort to get our heads above water, so we are not going to give up now and we are not going to fail for fear of not reaching the final.
"We will therefore manage it by telling ourselves that it would be a shame to put pressure on ourselves."
Oumar Diakite, who was sent off after celebrating his winner against Mali, is one of four players suspended for the semi-final, with Kossounou, Serge Aurier and Christian Kouame also banned.
Additional reporting by PA.