"Everyone talks about us as favourites but it also makes us a target," African Footballer of the Year Yaya Toure told Reuters after the Group D win at Rustenburg's Royal Bafokeng Sports Palace.
"Everyone is capable now of beating a big team and they all want to do so. We weren't surprised by how difficult it was against Togo.
"We knew of their qualities and the fact they beat Gabon in the qualifiers. It might have been a surprise to those who think we favourites but it was not for us."
Captain Didier Drogba has also gone out of his way to play down expectations.
"People want us to win all the games, but it's not possible," Drogba said after a subdued performance in his 91st international.
Gervinho, who scored the late winner, said his team had been fortunate.
"Nothing is easy at this level," he told reporters.
Toure was also impressed by Ethiopia in their 1-1 draw with defending champions Zambia.
"There are so many good teams at this competition," he said. "We watched Ethiopia play and we were impressed with the way they played with 10 men. They dominated the champions."
Ivory Coast are the top-ranked side on the continent. Their next group game is against Tunisia in Rustenburg on Saturday.