He wouldn't even have to admit he was wrong. He'd just need to say that from where he was standing it looked like there was illegal contact (or whatever). Nobody can argue with that, and even if video after the fact shows it wasn't a penalty, nobody can dispute what he thought he saw from his vantage point.
That way, fans at least get to hear his reasoning, and no admission of error needs to be made.
Unfortunately, given we operate in a footballing world where sections of fans vandalise houses and send live bullets through the mail, the chances of level-headed conversation is slim to none.