Dier saw red on Wednesday night and launched himself into the crowd to confront an abusive supporter.
Ahead of Tottenham's visit to Turf Moor at teatime on Saturday, Dyche said: "You manage a group of people but they are people and everyone has a moment when enough is enough.
"I don't know the details but if you think logically for a player to feel the need or urge to do that then it must have been something serious. On this occasion a player has decided that enough is enough.
"I have had it twice this year, only twice in a long time, and I am pretty thick-skinned.
"Twice this season I have thought it was too much and I have said to the person, not using any expletives, 'that is enough now' when it has gone too far. There are children in the stands as well.
"If it was two 18-year-olds then let it go, they're probably with their mates and we've all seen that. But this was two grown men and I thought 'whoa, hang on a minute'.
"Mine is two instances in thousands of very good moments with supporters both around stadiums and outside stadiums and when I am with my family and stuff.
"Most people are really good and they just want a chat and a bit of fun. It is only two moments I have had."
On both occasions, Dyche did not feel the need attract the attentions of the steward or take the matter further with the unnamed clubs in question.
He added: "No complaints or anything, no complaints to the clubs, just 'enough now, that's enough'. And they don't stop. Some do, some don't.
"We all understand that you pay your money and all that but that can't give you carte blanche to just say literally whatever you want to someone, I'm not sure that's quite right.
"Sometimes it's tongue-in-cheek personal and you know the difference. I've been around football all my life so I know the difference between when it's tongue-in-cheek and when it's too much.
"I don't know how you govern it or manage it but on this occasion it has highlighted where a moment goes too far.
"I must make it clear there's no drama from my point of view, fans have been very good to me, home and away."