A furious Moyes marched on to the pitch at the end and remonstrated with Atkinson for signalling time, just as Everton were threatening a third stoppage-time goal that would have given them an astonishing 4-3 win.
After berating Atkinson and gesturing angrily at him, the Everton managed brushed aside suggestions it could land him in hot water with FA disciplinary bosses.
In a rage: David Moyes argues with Martin Atkinson at Goodison Park
But Sportsmail has learned that Atkinson included the flashpoint in his match report and Moyes and his assistant Steve Round, who joined in the protest, have both been charged with improper conduct.
FA chiefs studied Atkinson's account of the incident before deciding to implement a charge of improper conduct, rather than the more serious offence of misconduct, which would have led to a two-game touchline ban.
Moyes and former England assistant-coach Round have until Thursday to respond to the charge. Under new legislation, they will each be fined £8,000, for a first offence, should they admit their guilt.
If they decide to contest it, they will appear at a hearing and argue their case, in the knowledge that they would face a stiffer financial penalty, if the outcome still goes against them.
Asked about his outburst at the time, and whether it might land him in trouble, he said: 'Well, if it does, fine, because at the end of the day someone has to turn round and say what they think. If you feel therehas been an injustice, you have to be able to air your views.
Temper: Moyes erupted over the decision to blow as Phil Jagielka attacked
'I'm just saying it was the wrong decision for football and the wrongdecision for me. He blew 10 seconds after deciding there was time for United to take a corner, and that can't be right.
'I didn't ask for an answer from him. I just told him he had made a wrong decision. I just think it was incorrect for football and for spectators who come along and pay to watch football.'
Everton 3 Man United 3: Not even Rooney can bend iron rule of Fergie Graham Poll: I was wrong at Everton. and 10 years later, so did AtkinsonEVERTON FC