Goals from Wes Morgan and Marc Albrighton saw the Foxes into the quarter-finals for the first time in the club's history, with Nasri receiving his marching orders in the second half following a clash with Vardy.
Nasri, though, felt Vardy had acted in a cowardly manner, claiming the forward dived to get him in trouble.
"He didn’t say anything but he played it well. We went face to face and then he fell on the floor," he told reporters.
"I thought the English player was tougher than that. He was the one who came to my face, and then went on the floor. He played it well.
"I didn’t touch him, I didn’t do anything with my head. He went on the floor and then the referee gave us both a yellow card.
"For me, he is a cheat. Because if he was a foreign player, you the English press would say he is a cheat.
"They were winning 2-0, play the game like a man. Win it. You are not better than us but you are winning 2-0, you will qualify, just play the game. You have quality, you are an international player, you don’t need to do that."
Nasri needed to be restrained following his dismissal, and seemed to gesture towards Vardy that he would speak to him after the game.
But the former France international was reluctant to reveal exactly what he would have told the Leicester man so as to avoid any further punishment.
"I would love to speak to him but you know too many cameras, too many security, and I have to think about next year and not getting a big suspension.
"We are not playing in the same league so it would be hard for me to get back at him. It doesn’t matter any more."