Zahoui, who has put the Elephants back on track after their first-round exit at the last World Cup, saw nothing wrong in a laboured 1-0 win over Sudan's team of home-based players on Sunday.
"Ivory Coast are always expected to put on some fireworks, but our target is to win the cup, which is a short and very, very difficult competition," he said.
"There are a lot of things we can improve on but this was positive as debuts go. The important thing is to win the Cup.
"I'm not saying that the way in which we do it is not important, but this win relieves the pressure."
The 2012 tournament in Equatorial Gabon and Gabon is seen as a last chance for Ivory Coast's current crop of players, several of whom - such as Didier Drogba, Salomon Kalou and Gervinho - have played in four or more tournaments, to win the title
"I was not surprised by Sudan's resistance," said Zahoui who enjoys an unbeaten 14-match record as coach including a 100 percent record in the Nations Cup qualifiers.
"I expected a very motivated team against us, you can never minimise another side. It was also important to keep another clean sheet."
