The unrest had been simmering in recent weeks.
Supporters are furious with the side's performances of late and many fear they have hit poor form at the wrong time with rivals steadily improving.
But this was not just a case of those tensions spilling over. These goals came in the second half after introducing Chris Wood in attack along with Ashley Barnes to give more presence to the Clarets attack.
Saturday's recall to the Hammers first team - his first start since last November - rekindled the keeper's hopes of a front seat on England's World Cup plane to Putin land.
Burnley were once as high as fourth and can close to within two points of Arsenal in sixth with victory over West Ham on Saturday before the Gunners meet Watford on Sunday. Michail Antonio rose from the bench to provide a goal and a small measure of dignity for the Hammers but while his display was enough to earn him a start this weekend, most of his teammates will need to improve if they're to keep their own place in the side. That was frustrating but this season I think I have played some good football. As soon as we go a goal down we get targeted.
Referee Lee Mason was also forced to stop the game shortly after when another supporter came on to the pitch, grabbed a corner flag and attempted to plant it in the centre circle.
Moyes added: "I think as a supporter you can't cross the line, as a supporter".
Newcastle won 3-0 at home to Southampton, with on-loan Brazilian Kenedy scoring twice, to move five points clear of the bottom three. Can we make improvements, can we play better, can we do things much better? - of course, we can.
"I'm not saying all West Ham fans but there are a lot of them in this stadium who are not happy and it's a tough atmosphere to play in". "Am I happy with the goals we conceded?" But to do it - it would really help everybody to pull in the one direction because we've got eight games left to do so and I think we are more than capable of doing it - we are going to have to prove it.