Television cameras and microphones caught Tomic directing a number of sexually explicit comments toward someone in the crowd during the first set of his 6-4 6-3 4-6 7-6(0) defeat to world number 72 Dzumhur.
The Australian, who was the 17th seed at the year's final grand slam, later apologised for his comments but suggested he was forced into it by the heckling he had received.
"He was just baiting me a bit," Tomic, who cold face a fine from the International Tennis Federation for his comments, told reporters. "I don't want to get into it. I apologise for what I said to him.
"He definitely baited me the whole set for me to say that. But I do apologise. If there were people around that heard, yeah, that's all I can say.
"I couldn’t care less. I apologise right now if anyone heard around, but I directed it specifically to him."
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The incident was the latest in a long list of controversies to affect the world's 19th ranked tennis player.
Tomic drew heavy criticism in May following his exit from the Madrid Open when, on match point against Fabio Fognini, he held the racquet by the strings and did not offer a shot to the Italian's serve.
The Australian, who was nicknamed 'Tomic the Tank Engine' after accusations he 'tanked' - or failed to try his best - in a loss to Andy Roddick at the 2012 U.S. Open, then told a News Corp. journalist who questioned his actions in Madrid "would you care if you were 23 and worth over $10 million (7.65 million pounds)?"
He later ruled himself out of consideration for the Rio Games after the head of the Australian team had warned him that his behaviour was being monitored to judge his suitability for the Olympics.
In 2013, Tomic lost his driving licence for speeding and in 2015 he was arrested in Miami for trespassing and resisting arrest after a party.
