Manchester United midfielder Fellaini raised his forearm and made contact with City defender 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.
"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."
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