Moyes has been punished in relation to post-match media comments he made following United's 2-1 League Cup semi-final first leg defeat at Sunderland on January 7.
Referee Andre Marriner came in for criticism from the Scot after he awarded Sunderland a second-half penalty - which was converted by Fabio Borini - for a foul on Adam Johnson by Tom Cleverley, although replays appeared to show contact had been made outside the box.
This followed on from a free-kick being given against United defender Jonny Evans in the first half, which led to Sunderland's opening goal.
Afterwards, Moyes claimed his team are "having to play officials as well as the opposition", adding: "It's terrible, it really is, we're actually beginning to laugh at them."
And, following an independent regulatory commission hearing on Friday, a statement on the FA's website read: "Manchester United manager David Moyes has been fined £8,000 and warned as to his future conduct.
"Moyes had admitted an FA misconduct charge in that his post-match comments following his side's game at Sunderland on Tuesday 7 January 2014 constituted improper conduct in that they 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 FA Rule E3(1)."
Moyes is the latest Premier League manager to face disciplinary action for speaking out against referees this season. Earlier this month, Brendan Rodgers was fined £8,000 for comments made following Liverpool's 2-1 defeat at Manchester City on December 26.
Rodgers labelled the performance of the officials as "horrendous" after the game at the Etihad Stadium.
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