Moyes and Round confronted referee Martin Atkinson at the end of the game after he had blown the final whistle while Everton broke away on the counter-attack. Everton had scored twice in injury time to rescue the point.
After the game, Moyes said: "The two goals were scored after 90 minutes and they'd put up three minutes of extra time. He didn't get his time right because there was more time to add on for the goals and he played three minutes 30 seconds.
"They had the corner kick and we had a great counter-attack and he blew up with the ball 25 yards from their goal. It is a spectator sport with people coming to watch the game and not for him to be the main man and the one who wants to be seen making the decisions.
"That was a terrible decision in my book."
The FA has now confirmed that Moyes and his assistant face disciplinary action over their response to the incident.
A statement read: "Everton manager David Moyes and assistant manager Steve Round have both been charged with improper conduct.
"The charges relate to Moyes' and Round's conduct towards referee Martin Atkinson on the pitch following the final whistle at Everton's home match against Manchester United on September 11.
"Under the FA's new fast-track procedures, Moyes and Round have until Thursday, September 16, to respond to the charges and have both been offered a standard sanction of an £8,000 fine should they accept the charge.
"If either party denies the charge, the case will be heard by a regulatory commission within 10 working days."