Nasri, who is on loan at Sevilla from Manchester City, was shown a second yellow card by Italian referee Daniele Orsato for violent conduct after squaring up to Vardy.
"For me he's a cheat because if he was a foreign player you, the English press, would be saying he's a cheat. For me he is a cheat," Nasri told reporters.
"They were winning 2-0, play the game like a man. You are not better than us but you are winning 2-0 and will qualify, just play the game."
Leicester came out in support of Vardy and the player also refuted the Frenchman's comments.
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"I'm not a cheat and I never have been. That's all I've got to say on the matter," Vardy was quoted as saying by the BBC.
A Leicester City spokesperson said: "The club refutes entirely any allegation that questions the professional integrity of Jamie or any of its players".
(Reporting by Hardik Vyas in Bengaluru; Editing by Peter Rutherford)
