Two Blackburn fans invaded the pitch after Clarets' second goal in the 27th-minute, and due to the late response from stadium stewards, Clarets players were left to defend themselves against the troublemakers. One of them tried to attack Ashley Westwood before he was tackled down by the midfielder.
Following the game, Dyche said: "There used to be a time when if people got on a football pitch it was kind of in jest, it could almost be laughed at.
"Now there's all kinds of things going on in the world, and when people get on a football pitch it has to be stopped very quickly. That's not just this football club, that's across the board. Stewards do a terrific job but they've got to get on quick.
"It seemed a long time before anyone did anything and then our players had to eventually defend themselves, and that can't be right anywhere in football. We were going to go on because I can't have that. Not to do anything ridiculous just to say 'this can't happen'.
"To think you go to the extreme (of escorting fans) and then someone just wanders onto a football pitch is a bit bizarre at least. The safety of players is paramount."