PSV hosted Ajax at the Philips Stadium on Sunday as both sides continue to challenge for the Eredivisie title.
Eran Zahavi fired PSV into the lead in the first half, but Tadic pulled back an equaliser after converting from a penalty in the 92nd minute.
However, Tadic ran over to PSV right-back Denzel Dumfries and celebrated in front of him after he beat Yvon Mvogo from the spot-kick.
Both Tadic and Dumfries were spotted arguing at the full-time whistle, with the Ajax star later claiming he had been insulted before he took the penalty.
Tadic explained: "I picked up the ball and put it down. Then three players came up to me, kicked the ground, and made a hole at the spot.
"Dumfries told me that I am a p***y, that I am not a leader, that I was going to miss.
"So, what should I do if I score afterwards? Say to him, 'Thanks for calling me a p***y?' No, then you say the same back."
However, scenes turned ugly as furious PSV fans waited for Tadic and proceeded to hurl coins at him as he tried to board the Ajax bus.
Fans were stood behind railings outside the Philips Stadium as they were unable to attend the match live amid the coronavirus pandemic.
A clip from the incident has now circulated on social media, which showed a fan hitting the 32-year-old Serbian on the side of the head with a coin.
Tadic then covered his head to avoid any other coins as he was scurried onto the Ajax bus.
Dumfries slammed Tadic by claiming that the Serbia international had insulted his mother on the day.
The 24-year-old Dutchman explained: "I don't want to point the finger right now, but you shouldn't talk about my mother.
"I do not appreciate that and you just should not do that, it does not belong on the football field or next to it.
"If you call me names, I'm fine with it. But don't say things like that."
Ajax are top of the Eredivisie table and hold a six-point lead over second-place PSV.
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