The Manchester City midfielder insulted a journalist and challenged him to a fight during a heated exchange in the mixed zone after the Bleus' 2-0 loss.
The French football federation (FFF) has reportedly opened an investigation into the 25-year-old's actions, and Nasri could face a two-year ban from the national side following his outburst.
"Too many false truths are circulating at the moment," Nasri said on Twitter. "I want the supporters, particularly children, to know I sincerely regret that my words could have shocked them.
"I love the French football team, football and I have a profound respect for the public. For the rest, it was a personal issue between me and a few journalists. I will explain myself when the moment is right."
Once again, France's campaign in Poland and Ukraine was marred by controversy, with Nasri's outburst and clashes in the dressing room after the 2-0 loss to Sweden among the incidents reported.
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