Moyes will now face a fine or a warning following a disciplinary hearing, which will take place in due course and he has chosen not to attend.
Moyes was charged after speaking out in the aftermath of his side's Capital One Cup semi-final first leg loss at Sunderland last week.
The Scot said United "were playing referees as well as the opposition" after a number of decisions went against his side in the 2-1 defeat at the Stadium of Light.
Moyes suggested his side had endured a run of bad decisions, a situation he described as "terrible" and that they were "actually beginning to laugh" at.
At Sunderland, Moyes was particularly irritated by referee Andre Marriner's award of a free-kick - which United failed to defend and from which they conceded an own goal - and what proved the match-winning penalty to Sunderland.
The FA charged Moyes on the grounds that his remarks "allegedly called into question the integrity of the match officials appointed to that fixture and/or appointed to Manchester United fixtures generally, and/or implied that such match officials are motivated by bias; and/or brought the game into disrepute, in contravention of Rule E3(1)."
The matter comes a week after Liverpool manager Brendan Rodgers was fined £8,000 by the FA for questioning the appointment of referee Lee Mason to his side's Boxing Day game at Manchester City.