The Manchester United midfielder raised his forearm and made contact with Zabaleta's face in the first half of his team's 3-0 defeat at Old Trafford on Tuesday.
Referee Michael Oliver deemed the incident worthy of only a yellow card, when many suggested Fellaini was perhaps lucky not to receive a red.
However, the Belgium international has insisted he meant his opponent no harm, and even claimed Zabaleta simply "bounced against" his arm.
"I certainly didn't do it on purpose," Fellaini told the Daily Mail. "I put my arm up to try and protect possession of the ball, and Zabaleta bounced against it.
"He was unlucky to make contact. The movement by me was not in an aggressive manner. It was a defensive move to protect the ball."
United's defeat to City means they currently lie in seventh, 12 points behind fourth-placed Arsenal.