The Terriers took the lead through Josh Koroma just before half-time.
However, a Will Keane penalty and a late seven-minute hat-trick from Milutin Osmajic saw Preston claim all three points.
The defeat left Huddersfield on the brink of the relegation zone, only above Sheffield Wednesday on goal difference.
Terriers winger Burgzorg approached the travelling fans at full-time to give away his shirt.
However, he quickly got into a heated discussion with a small group of supporters.
The Dutchman was filmed urging fans to show the team more respect.
However, he was met by a furious response.
One supporter took to social media to share the clip, writing: “So disappointed in Della wow. #htafc.”
But some were quick to defend Burgzorg, with one person commenting: “At least he comes over to hear fans out, not like rest of them.”
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Another added: “‘Fans’ these days are a f*****g disgrace, meant to support, encourage and be together through absolutely everything.”
While a third wrote: “Is one of our best players. Why are you disappointed all he’s asking is to show some respect?”
Huddersfield are next in action on Saturday when they face Bristol City at Ashton Gate.