Despite calls for a sending-off, referee Michael Oliver issued the Belgium international with a booking instead.
According to the Daily Mail, when asked if he was lucky to escape with just a yellow card, Fellaini said: "I don't know, but I certainly didn't do it on purpose.
"I put my arm up to try and protect possession of the ball, and Zabaleta bounced [his jaw] 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 are currently seventh in the Premier League table, 12 points adrift of a Champions League spot.