The Gunners looked on course for a fourth straight Premier League win after Pierre-Emerick Aubameyang opened the scoring and the home side then created a string of chances to kill off the game.
Instead, they had to settle for a 1-1 draw as Vardy scored with six minutes remaining, soon after Arsenal had been reduced to 10 men following the dismissal of Eddie Nketiah.
The Arsenal forward had only been on the pitch for four minutes when referee Chris Kavanagh showed him a red after reviewing a foul on James Justin using his pitchside monitor.
“I have my opinion, I prefer to keep it like this,” he said.
“What I am saying is if you review incidents of that type you should review them all.”
“If Eddie’s is a red card then for sure the other is a red card.”
“If (Nketiah) can be a red card then Leicester has to play with 10 men after 42 minutes – that has to be a red card as well.”