West Ham supporters have a right to protest against their owners David Gold and David Sullivan, the Daily Telegraph's Chief Football Writer Sam Wallace told the Sunday Supplement.
Numerous pitch invasions marred Burnley's 3-0 victory over David Moyes' side, with Mark Noble admitting he had to protect himself against invasive supporters.
Investigations are underway by the club and Premier League, and an emergency meeting of all stakeholders has been called following the ugly scenes on Saturday.
Wallace condemned the disorder and lack of police presence, and believes disgruntled fans must strike the right balance between protesting without endangering those inside the stadium.
He said: "It's not nice to see children being sheltered in the away dug-out and it's a head-in-hands moment when a middle-aged man gets on the pitch and waves a flag around.
"It's right that we condemn this behaviour because it took us many years to get rid of hooliganism from the game.
"But we shouldn't lose sight of the fact that football fans in this country have always had the right to protest.
"There's a strong tradition of that and I would always want fans to stand up for their club. But we have to balance this with not putting people in danger. Running on the pitch sends a bleak message.
"Fans have a right to protest, but going on the pitch is a red line and it's wrong for children to feel in danger."
West Ham's day of shame was sparked after Ashley Barnes had given Burnley the lead with a fine strike and the revolt which ensued has dominated Sunday's papers.
The Hammers are 16th in the Premier League following a third straight defeat, with Southampton at home up next at the end of the month.
Wallace claims that West Ham supporters feel they have been lied to over false promises that have led to legitimate grievances.
He added: "The problem with West Ham's stadium is that it was built for the Olympics. There was no legacy for football. It's been a terrible compromise that hasn't worked for anyone, least of all the taxpayer.
"Right from the offset, there didn't seem to be a plan. West Ham felt they couldn't turn it down because financially it was great but even the walk to the ground, it doesn't feel like a community.
"I think they're facing a game behind closed doors. It pains me but I think that would be the right decision. Fans on the pitch creates an atmosphere of the days of anarchy.
"If you can't control people coming on the pitch then you can't control the stands. The club has got to be better run. Part of the investigation has to include the owners looking at themselves."
There has been an undercurrent of discontent at West Ham throughout the season with many having serious issues with co-owners Sullivan and Gold.
The club spent a club-record £80m on players during the 2016/17 season, but investment has levelled off over the past 12 months.
The Hammers have the seventh-highest wage bill in Premier League, but Gold and Sullivan have received £14.8m interest on loans to the club since 2011.
Jeremy Cross, Chief Sports Writer at the Daily Star, feels the disconnect between the owners and supporters is at the heart of the matter.
He said: "It comes back to the ownership of the club and they are clearly two very unpopular guys.
"The fans feel they've lost their identity moving to the London Stadium. It's been a fiasco. They've had a net spend of under £30m this season, and that's a pittance by Premier League standards.
"They have a mediocre team with not a lot of talent, and they are where they are for a reason. The fans feel they've been lied to."