The sanction, the same as handed out to Liverpool boss Brendan Rodgers for his criticism of referees, comes after Moyes said United were "playing referees as well as the opposition" following his side's third defeat in a row.
An FA independent regulatory commission imposed the punishment on Friday.
An FA statement read: "Manchester United manager David Moyes has been fined £8,000 and warned as to his future conduct following an independent regulatory commission hearing today.
"Moyes had admitted an FA misconduct charge in that his post-match comments following his side's game at Sunderland on Tuesday January 7 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 issued his criticism after questioning the awarding of a free-kick that led to Sunderland's opening goal and the later award of the match-winning penalty.
He said: "I feel we are having to play the opposition and the referees. We are all just laughing at them at the minute."
The incident followed the United manager saying it was "scandalous" his side were not awarded a late penalty against Tottenham at Old Trafford last month.