The Terriers climbed off the bottom of the Premier League table after Christopher Schindler cancelled out Sam Vokes’ opener but it was two off-the-ball incidents that provided the main talking points.
The game was delayed for more than five minutes in the second half while Schindler received treatment after taking an elbow in the face from Vokes.
To rub salt in the wound, the German defender then blocked a shot from Ashley Westwood with his face and Huddersfield’s medical staff had to work hard to stop the bleeding from two cuts, one on the bridge of his nose and one under his right eye.
The Football Association could well take a second look, with referee Christopher Kavanagh taking no action at the time.
Wagner was inclined to give Vokes the benefit of the doubt in terms of intent, but said: “This is nothing I like to see in football.
“I don’t like to say that opponents do it on purpose but they have to have better control over their bodies. This is too dangerous, this is ugly.”
Dyche did not feel it was anything more than an accident at the time and insisted it was not in Vokes’ character to make a deliberate action.
Wagner felt the same about Laurent Depoitre’s second-half dive, which Kavanagh did punish with a yellow card and left Dyche irate.
The Burnley boss gave an impassioned polemic on the subject at his pre-match press conference and the yellow card did nothing to placate him.
The Burnley boss said: “A yellow card isn’t going to make a difference. Is anyone going to do it next week? Yes.
“That’s absolutely embarrassing. We’re not talking about gamesmanship, we’re talking about blatant dives, and today was cringeworthy. But no one wants to do anything about it apart from me it seems.”
Dyche wants players either to be red-carded or face retrospective punishment.
“Ban them, every single time,” he said. “Because it’ll disappear. If he’s seen it well enough to book him, just send him off.”
Wagner said he would speak to Depoitre, adding: “This is of course something else that we don’t like to see. Like these ugly elbow challenges, we don’t like to see diving.”
Huddersfield came away from the game with a fourth goal of the season and third point, but Wagner justifiably felt they deserved more after having more than two-thirds of the possession and 19 shots to Burnley’s six.
“This was a very good, very strong performance,” said the Terriers boss. “We looked brave, we looked confident, we played very good football, we controlled and dominated as well most parts of the game.
“We were able to come back from 1-0 down and the least we deserved was a point. We should have had three but we’ll take it.”
Dyche felt aggrieved that Vokes did not get a penalty in the first half when he appeared to be pulled back but accepted his side were below their best.
The Burnley boss said: “First half, very good, game should have been out of sight, three golden chances at this level.
“Second half, they didn’t relent. We thought they might be a bit brittle with all that’s gone on, but they kept playing, forcing us back. We lost our way, that was quite obvious.”
James Tarkowski, meanwhile, is a doubt for England because of an ongoing groin problem.
He was ruled fit enough to face the Terriers, but Dyche said: “We’ll see how that settles down overnight and then he’ll make a decision with the medical team.”