The incident saw Wiley penalise Stoke defender Leon Cort for handling the ball but, after consultation with his assistant, he awarded Everton a free-kick outside of the area instead of a penalty.
Television replays backed Moyes' view that Cort had handled inside the box.
Moyes watched the last 15 minutes of the game among Stoke fans but insisted afterwards that he had not sworn at the officials.
The Everton boss was charged by the FA on 17 September and revealed that Wiley had spoken to him about the incident.
"The referee has since contacted me - that conversation will remain private - and that is it," Moyes explained.
"We have a Respect campaign that is really important but you can't just put a big label on it. You earn respect and I have to say the referee has earned a great deal more respect from me by what he has said from me."
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