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
In 2006, Ivory Coast went all the way to the final but lost on penalty to hosts Egypt.
Two years after that in Ghana, they looked unstoppable as the goals flowed until they were again confronted by Egypt in the semi-finals and were promptly thumped 4-1.
The 2010 tournament saw them outplay Ghana 3-1 in the group stage, only to lose to Algeria in the quarter-finals.
Having seen Nigeria, Cameroon and Egypt all fail to qualify and then Equatorial Guinea and Zambia pull off shock wins on Saturday, Zahoui was aware of the pitfalls awaiting his side.
"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."
