The Scandinavian side appeared to be on the road to victory on Saturday when Ola Toivonen lobbed over Manuel Neuer in the first half.
Marco Reus, however, levelled the game after half-time before a stunning effort from Toni Kroos in injury time gave the World Cup holders three crucial points in the Group F showdown.
Durmaz had committed the original infraction that led to Kroos' strike and, after the game, a flood of offensive comments were sent to his Instagram account.
The Toulouse player, who was born in Sweden to parents of Assyrian heritage who emigrated to the country from Turkey, was targeted with slurs like "terrorist", "Arab devil" and "Taliban warrior" in the aftermath of the defeat, and also received death threats, although hundreds of other commenters paid tribute to the star and slammed the racist attitudes espoused in the post.
"It's nothing I'm bothered about," he told reporters when questioned on the abuse. "I'm here proud and representing my country."
Later, however, Durmaz hit out at those who had used his heritage to insult him, dubbing the situation "completely unacceptable."
"I am a player at the highest level, being criticised is something we are used to, it is part of the job and we have it every day," he said.
"But to be called a suicide bomber and to say you will kill me and my children is completely unacceptable. I am Swedish and I carry my shirt and flag with pride.
"I would also like to thank all of those wonderful people who have spread joy. We are united, we are Sweden."