West Ham now sit in 14th place on 30 points just three clear of the Premier League drop zone and were dealt a huge blow earlier this week when key defender Winston Reid was ruled out for the rest of the season after picking up a nasty knee injury at Swansea last Saturday.
A West Ham statement said: "We have immediately launched a full and thorough investigation into the incidents which marred the second half of today's match and are committed to taking decisive and appropriate action".
There were also further stoppages in play after both of Wood's goals, with one intruder planting the corner flag in the centre circle in a show of frustration.
Once more the stewards were seemingly powerless to intervene except to ask West Ham joint-owners David Gold and David Sullivan, whose decision to quit the east London club's longstanding Upton Park ground for a move to what was the 2012 Olympic Stadium is a source of some fans' fury, to leave their seats, seemingly for their own safety.
"No, not at any time", Moyes said at a post-match news conference.
Things went absolutely bonkers at the London Stadium on Saturday afternoon, after frustrated West Ham fans swarmed the directors' box in protest during the loss to Burnley.
"We were one goal down, in with a real good chance still - you know, the game was really tight".
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The beleaguered Scotsman was clearly shaken by the series of events that came hand-in-hand with another second-half capitulation as visitors Burnley eased to a 3-0 Premier League victory at the London Stadium. That was frustrating but this season I think I have played some good football.
"Overall I have worked higher up but I would say it's the most competitive it's been".
"But the rule is that you can not come on to the pitch - you're not allowed".
"An emergency meeting has been called with all London Stadium stakeholders". They're fighting for points, we're now fighting for points for different reasons.
"Joe made a mistake - we can't dress that up in any different way", added Moyes.
Burnley's recent 11-match winless run, brought to an end with a 2-1 win over Everton last weekend, was the third longest of its kind in the Premier League this season. "To get to 40 points at this stage of the season is very pleasing and the lads have earned the right to do that".
"They just want to see their team win".