Goals from captain Wes Morgan and Marc Albrighton saw Leicester overturn a 2-1 first-leg deficit with a stirring performance, roared on by a fervent home crowd.
Vardy's relentless running from the front set the tone for Craig Shakespeare's side and ensured it was a torrid evening for Sevilla's defence.
However, it was the England international's role in an off-the-ball incident with Nasri in the 74th minute that arguably did the most harm to the Liga high-flyers' prospects of reaching the quarter-finals.
Nasri, already booked for a first-half foul on Wilfred Ndidi, put his head towards Vardy following an altercation and was unimpressed by the manner in which his opponent went to ground – questioning the 30-year-old's toughness.
"He didn't say anything but he played it well," the on-loan Manchester City midfielder told reporters.
"We went face to face and then he fell on the floor. 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 reacted but 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."
Asked whether he thought Vardy dived to get him sent off, Nasri responded: "You don't think so? Look at the image.
"Yes he did it, but he did it well. I should have thought about it before and been smarter.
"For me, he is a cheat, because if he was a foreign player, you in the English press would say he is a cheat. For me, 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 gestured towards the players' tunnel after seeing red and he was unable to conceal still simmering anger towards Vardy afterwards, apparently with retribution in mind.
"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.
"What would I say? You would not be able to write it."
Nasri faces an uncertain future when his season-long stay at Sevilla ends, and the prospect of an on-field reunion with Vardy is not a motivation for him to come racing back to England.
"I don't know what's going to happen in the future, I am enjoying my time here so we will see," he added.
"[Playing against Vardy again] doesn't matter, we are not playing in the same zone so it would be hard for me to get back at him. It doesn't matter anymore."