"Too many untruths circulate at the moment. May the fans, and the children in particular, know that I regret sincerely that my words may have shocked," he said on his Twitter feed.
Nasri, who was a second-half substitute in France's 2-0 defeat by world and European champions Spain, passed waiting reporters without saying a word after the match.
Asked by one journalist for a quote, he answered: "You are looking for s***, you are looking for trouble."
The reporter replied: "Get lost, then, if you have nothing to say."
Nasri turned back and said "f*** you" followed by a stream of further abuse, inviting the reporter to have a conversation with him man-to-man.
"I love the France team, I love football and I have deep respect for the fans. For the rest, it's a personal matter between me and some journalists. I will explain myself in due time," Nasri added.