Nasri, who came in as a second-half substitute, went through the mixed zone without a word for text reporters after the match.
Asked by a reporter for a quote, he answered: "You are looking for s***, you are looking for trouble."
The reporter replied: "Get lost."
Nasri then 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.
"There, now you'll be able to say I've been badly brought up," Nasri added.
His manager Laurent Blanc criticised both parties after the incident on French television.
"Above all there's a problem between Samir Nasri and the press," Blanc told TF1. "It's regrettable but the true problem is with the press.
"The reality of the words are there. They are very violent words. There is a lack of respect vis-a-vis a journalist.
"But the journalist did not have that much respect either at the time."
It concludes a tournament for the Frenchman when he has constantly been at odds with his national press.
Nasri had already been involved in a row with the media at the tournament when he muttered "shut up" after scoring the equaliser in France's 1-1 draw against England in their opening game.
He explained at the time that the celebration had been aimed at a journalist from French newspaper L'Equipe.
"He asked me who the insult was aimed at, I said it was for him," Nasri said after the game.
"It was frustration. I was shot down in flames after the warm-up matches for following the coach's instructions," he added later.
After France's opening game against England, some French journalists stayed on in the mixed zone for two hours after the match to speak to the goalscorer, only to be told by Nasri: "I didn't ask you to wait."