Nasri, 29, was dismissed for a second yellow card in Sevilla’s 2-0 last-16 second-leg defeat, as the Foxes reached the quarter-finals 3-2 on aggregate.
Nasri and Vardy clashed in the second half and were booked for butting heads.
But the on-loan Manchester City star believes Vardy’s response convinced referee Daniele Orsato to take action.
“For me he’s a cheat because if he was a foreign player you, the English press, would be saying he’s a cheat,” he said.
“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.”
But England striker Vardy refuted Nasri’s allegation, saying: “I’m not a cheat and I never have been. That’s all I’ve got to say on the matter.”
A Leicester spokesman added: “The club refutes entirely any allegation that questions the professional integrity of Jamie or any of its players.”