"I don't know what I'm allowed to do now that the referee has said he won't change his mind. But I'm determined to appeal," Livingstone told the Grimsby Evening Telegraph.
"I'm not injured, haven't done anything wrong and now I'm being told that I've got to miss three games. It's a situation I've never been in before and I'll do everything I can to fight it.
"I've seen the video and my forearm does come across his body as leverage so that I can hold him off and get past him. But I don't what the referee has seen.
"There's no sign of me throwing an elbow at him. But referees very rarely change their minds and I didn't expect him to.
"In that case I don't think the FA will go against the referee. They'll just back him up."