Moyes was infuriated by the decision of referee Andre Marriner to award Sunderland a free-kick following the aerial challenge between Jonny Evans and Stephen Fletcher which led to the home side's opening goal.
And he was equally scathing of the official after midfielder Tom Cleverley was adjudged to have fouled Adam Johnson in the box, resulting in Fabio Borini's match-winning penalty.
The defeat, United's third in a row, equalled their worst run in 13 years and after the match a furious Moyes said: "It's really terrible, it really is, we're actually beginning to laugh at them.
"We just need to keep going, we didn't do an awful lot wrong. We conceded a terrible first goal from the free-kick, but it was never a free-kick, it was our free-kick.
"I thought the referee was going to blow in our direction. I couldn't believe he gave a free-kick for that Jonny Evans challenge on Fletcher in the air, it was just a terrible decision.
"We've got an opposition to play and sometimes we've got other people to play at the moment."
The outburst follows a few days after Moyes claimed it was a 'scandalous' decision not to award a late penalty for his side after Tottenham keeper Hugo Lloris appeared to upend Ashley Young in the box at Old Trafford on January 1.
And the FA has also said it will investigate at least two incidents involving flares and smoke bombs during Sunderland's 2-1 victory at the Stadium of Light.
No arrests were made on the night but Northumbria Police have revealed 'inquiries are ongoing to identify those responsible'.
An FA spokesman said: "We are looking into David Moyes' comments to the media following the match at Sunderland.
"We are also contacting both clubs to seek their observations in relation to the use of flares last night."