Chris Wood's double from the bench was overshadowed by a toxic atmosphere as co-chairmen David Gold and David Sullivan were escorted out of the directors' box for their safety with supporters chanting about the club's leadership.
The Premier League said: "It is essential that everybody who plays or attends a Premier League football match can do so safely". I didn't even look around to see if there was anybody there.
"I don't think there's a good time to play any Premier League team because you don't know when they're in a good spell or a bad spell", Moyes said.
"The supporters will have their reasons for it".
"I didn't feel under threat - they were just voicing their frustration". The team has played well too, so it has all come together.
"There is no place at any level of the game for what happened at the London Stadium today".
While the Clarets have had a year to forget so far, they picked up their first win of 2018 last weekend, coming from behind to clinch victory for the first time this season.
Those two away defeats on the bounce have left the Hammers in 14th place, just three points above the relegation zone, heading into another crucial weekend in the Premier League. I wouldn't use that as an excuse for me after it, but I certainly don't think it helped.
But back-to-back 4-1 defeats to Liverpool and relegation rivals Swansea City has dragged the Hammers back into the thick of things in one of the most congested survival battles in recent memory.
"It was ideal in relation to what the game gave us", said United manager Jose Mourinho, who won the tactical battle over rival manager Juergen Klopp.
Scott Arfield could be fit to return from a calf injury after missing the last two games.
"Joe Hart will start, " Moyes confirmed.
He has told the board that he will want to make major changes to the squad if he stays, with as many as 10 players leaving.