Ozil announced that he would be stepping down from Germany duty following his country's humiliating World Cup group stage exit.
He cited "racism and disrespect" as the reasons behind his decision, stating that "I am German when we win, but I am an immigrant when we lose."
Ozil's decision has sparked a heated debate in Germany, with Bayern Munich president Uli Hoeness insisting that "he has been sh*t for years" , while the German Football Federation issued a strong rebuttal of his claim of racism.
Turkish president Recep Tayyip Erdogan, with whom Ozil took a controversial picture before the World Cup, has backed the playmaker's decision, believing it to be "national and native" , but Bobic insists that the 29-year-old has shown his true colours.
"I think that's a bit cowardly," he told Bild am Sonntag .
"Ozil's criticism of social media, especially in the direction of the German Football Association (DFB), is unbearable.
"This blanket charge of racism simply does not correspond to reality. "
"He could have given an interview somewhere, live on TV. For us footballers, the rule is 'be a man and stand up.'"
Bobic believes that Ozil's photo with Erdogan, which he has defended , was a severe mistake, and does not believe that an experienced player should have been in such a situation.
"I would allow that to a player who is 18 or 19 years old, but a player who has been in the business for so long, 29 years old and world champion, needs to know what this looks like," Bobic said.
"If he does not know that, then he is either totally naive - I cannot imagine that - or it is calculating and he wanted to be provocative, or else he is alienated, of course, I understand the two hearts that beat in his chest, but nevertheless, you must know that you have a great responsibility."