With Togo out of the competition following a deadly gun attack on their team bus, three teams are battling it out for the two quarter-final spots from the group and defeat against Ghana on Friday could send the Elephants packing.
The Ivorians dominated on Monday but failed to convert any of their chances and now need a win against Ghana.
"We are disappointed but it's not over yet," coach Vahid Halilhodzic told reporters. "We lacked a bit of luck.
"Togo being out causes us problems. It will be a difficult match against Ghana but we have our fate in our hands."
Attacking talisman Didier Drogba said: "It is a complicated task but it is complicated for everyone."
Ivory Coast, who won their only Nations Cup in 1992, will have to be more efficient against Ghana.
On Monday Bakary Kone was a handful for the Burkina defence but failed to convert three clear chances and missed an open goal deep into the second half.
Chelsea striker Drogba made a lively start, having been denied a penalty in the third minute, before fading away.
"Sometimes it just does not work," said Halilhodzic who added he was satisfied with his team's overall performance.
Manchester City defender Kolo Toure was hopeful the Ivorians could turn the situation around.
"I am confident. We are going to work hard to be ready against one of the best teams in Africa," he said.
"We need to show character. We have the spirit, the team."
