Stung by some pre-tournament criticism from L'Equipe, the Manchester City man caused controversy by aiming a succession of curse words at the press box after netting against England in Les Bleus' tournament opener.
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Nasri was back in the headlines on Sunday morning for challenging a French journalist to a fight during a heated exchange in the mixed zone in Donetsk after his side's 2-0 defeat by La Roja.
"Yes, it is embarrassing if it really happened," Blanc told TF1. "If it is true, it is a lack of respect toward the journalist. But the journalist seems to have also disrespected Nasri. There is a problem between Samir Nasri and the press.
"It is regrettable for his personal image and for that of the national team. A coach needs to deal with his players' reactions to the press, but I already told Nasri what I had to tell him and visibly the message did not go through properly."
Nasri, who has 35 international caps to his name, was dropped from the starting line-up for the game against defending champions Spain due to a dispute after the loss to Sweden in the final round of the group stages.