The result left Burnley stuck in the Premier League relegation zone in 18th place.
"I was upset with the referee today because I think these are clear things," Dyche told reporters, accusing Arsenal's Matteo Guendouzi and Granit Xhaka of going down too easily.
"No-one seems to want to do anything about the diving except for me. I'm still amazed by it," he said.
He said the FA and the Premier League should take action, suggesting that banning players would soon eradicate simulation in the game.
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"You wouldn't ruffle your kid's hair when they come back from school if they've cheated in a maths test. If they cheat in a game of football then it's okay.
"There's hundreds of millions of pounds at stake in this game, and we've got all kinds of gadgets and everything to view these things and hopefully VAR will make a difference... I'm talking about the morality of the game," he said.
Dyche appeared to suggest that one cause of the problem was the influence of foreign players in the Premier League, citing the examples of former Chelsea star Didier Drogba and Spurs marksman Juergen Klinsmann, both of whom he said were nevertheless great players.
"When they came over and they were diving, it was on Match of the Day every week: 'We can't have this', and fans in uproar everywhere... and they slowly morphed into our culture here. Now it's every week and no-one hardly mentions it."
He was, however, keen to make a distinction between diving and gamesmanship, or going down from relatively light tackles.
"We're talking about blatant diving -- people who've had no contact at all and people going over," he said.
"My point is this: I'm a father, I've got a child who plays football, and I see children copying professionals and diving all over the place. That cannot be right," he said.
(Reporting by Hugh Lawson; editing by Clare Fallon)
