Fans approach players during West Ham's defeat by Burnley at London Stadium
West Ham have launched an immediate inquiry after supporters invaded the pitch during Saturday's 3-0 home defeat by Burnley in the Premier League.
At least two fans went onto the pitch after Burnley took the lead - with one approaching United's Mark Noble.
Another fan ran on with a corner flag shortly after Burnley scored their second, with further incursions after the visitors struck a late third.
Noble admitted that the atmosphere at London Stadium was "horrible".
The Hammers' captain said he did not feel in "danger" but that it was necessary to defend himself.
"I'm a West Ham fan and I've always protected the club," he said. "If someone approaches me, I'll protect myself.
"It's been like this for the past two seasons, since we moved to this stadium.
"Every time we lose we and the board get a lot of stick. It seemed today that the fans had had enough.
"They wanted to show their emotion. When fans come to the game with the hump, they know how to show their emotions.
"The atmosphere was horrible. We know a lot of it isn't aimed at the players, but we have to be man enough to play in that atmosphere."
Noble, 30, called for supporters to put their animosity towards the club's board aside until the season is over.
"I'm really hoping the fans have got it off their chest. They are a true, honest and passionate bunch of people. I'm hoping that they have had their outburst, because all that matters is staying in the Premier League," he added.
"If they can help us get over the line, maybe we can sort it out in the summer."
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Police said there were four separate pitch invasions and that they have received two allegations of assault which they said are being investigated.
West Ham want a police presence at all their remaining home games, starting with next one against Southampton on 31 March.
Shortly after the game West Ham released a statement which revealed that an emergency meeting was planned.
It said: "West Ham United 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.
"An emergency meeting has been called with all London Stadium stakeholders. There will be no further comment at this time."
The Football Association also released a statement saying it "strongly condemns the crowd disturbances seen at West Ham United versus Burnley and will be seeking observations from West Ham as well as awaiting the match referee's report".
In their own statement, the Premier League said: "It is essential that everybody who plays or attends a Premier League football match can do so safely.
"There is no place at any level of the game for what happened at the London Stadium today.
"While the official investigation of the incidents will be carried out by the Football Association, we will be asking our own questions of West Ham United about what happened this afternoon, especially to ensure similar events never reoccur.
"We would like to commend referee Lee Mason and his team of officials for their actions which, combined with the cooperation of players and coaching staff from both clubs, enabled the match to be completed."
In his post-match interview West Ham boss David Moyes said: "We want the supporters behind us, since I've been here they've been really good. But you can't cross the line and come on the pitch.
"A lot of my players did well with the way they acted."
Burnley striker Chris Wood, who scored twice, said: "It was a tough situation - I can sympathise with how the fans feel, they are passionate supporters and it is tough for them at the moment but they need to stick with their players.
"You don't want that happening on the pitch at all - it creates problems and safety issues.
"I didn't feel under threat - they were just voicing their frustration."
There were protests against the board and joint-chairman David Sullivan was escorted from his seat before the end of the match.
Burnley substitutes allowed some children caught up in the protests to sit on the bench towards the end of the match.
The result on Saturday was West Ham's third consecutive Premier League defeat - with two 4-1 losses preceding Saturday's game.
Moyes' Hammers are now 16th in the Premier League table, three points above the relegation zone.