"I told the players this morning we had to choose between two different paths, heaven or hell," coach Vahid Halilhodzic told reporters. "A draw or a defeat would have been a catastrophe.
"The fans, the whole nation would not have forgiven us. You can't imagine how tremendous the pressure was before the game."
Ivory Coast, held 0-0 by Burkina Faso in their opening Group B game on Monday, would have been on the brink of elimination had they not beaten Ghana.
The Ivorians now lead the group with four points from two games, with Burkina Faso second on one point and Ghana in last position in the three-team group.
Ivory Coast went 3-0 up through Gervinho, Siaka Tiene and Didier Drogba but also had defender Emmanuel Eboue sent off for a nasty tackle in the 56th minute.
"Scoring two goals when we were down to 10 men shows a great team is hatching," added Halilhodzic.
Drogba said: "It was difficult for us but we stayed compact."
Ghana must now beat Burkina Faso on Tuesday to progress after the group was reduced to three teams when Togo withdrew following a deadly attack on their team bus last week.
"They (Ivory Coast) were more experienced," said coach Milovan Rajevac.
Four members of last October's under-20 World Cup-winning squad started the game for Ghana, who are in Angola without experienced defenders John Mensah and John Pantsil.
"Quality and experience was the key of Ivory Coast's team. For us now it is, to be or not to be," said Rajevac.
"We must do our best to prepare for this game (against Burkina Faso) and win it."
