The Scot's punishment is relation to post-match comments to the media which he made following his side's 2-1 defeat in the first leg of their Capital One Cup semi-final at Sunderland on January 7.
Referee Andre Marriner came in for criticism from Moyes after he awarded the Black Cats a second-half penalty - which was converted by Fabio Borini - for a foul on Adam Johnson by Tom Cleverley, although replays appeared to show that 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.
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Following an independent regulatory commission hearing on Friday, a statement on the FA's official 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, January 7, 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 in January, Brendan Rodgers was fined £8,000 for comments made following Liverpool's 2-1 defeat at Manchester City on December 26.
Rodgers labelled the officials' performance as "horrendous" after the game at the Etihad Stadium.