The host nation looked to be heading out of the tournament in the pool stages after a humiliating 4-0 loss to Equatorial Guinea in their final group game.
But results elsewhere saw them squeeze into the last 16 with the 16th-best record of the qualifiers, though not before they sacked French coach Jean-Louis Gasset and replaced him with assistant coach Emerse Fae.
A penalty shootout victory over defending champions Senegal was followed by a 2-1 quarter-final success against Mali and a 1-0 semi-final win over Democratic Republic of Congo for a place in the decider against Nigeria on Sunday - a scenario that had seemed fanciful a few weeks ago.
"As long as you still have a five or 10 percent chance you need to keep believing, because that is what makes football beautiful," Kessie said.
"After the Morocco result (a 1-0 win over Zambia in the group stages), we knew we had qualified and that changed everything.
"It gave us the strength we needed, it boosted us. We knew we couldn't do worse than in the first round. We need to keep going like this because you can't go all the way to the final only to then give up."
Fae admits their run to the decider has been a surprise even for the team based on their form at the start of the tournament.
"We are happy, we're really moved," Fae said. "It's like a dream, when you go back two weeks to the defeat against Equatorial Guinea. It was hard then to imagine that we might qualify for the final of our own Cup of Nations."
Ivory Coast have reached a fifth Cup of Nations decider. All four of their previous finals have gone to a penalty shoot-out, winning two (1992 & 2015) and losing two (2006 & 2012).
