The Foxed grabbed a 1-0 away win over Arsenal thanks to an 80th minute header from Vardy.
Speaking to BBC Sport, Rodgers said: "The boys were outstanding, our idea against top quality players and you have to deny them space. You set up slightly different for the game. They executed it really well.
"I just felt Kelechi Iheanacho's strength is he can hold the ball up but with Harvey Barnes he can stretch the game. He did not have quite as many opportunities but our plan was always to bring Jamie Vardy into the game and he can stretch it. The goal was a fantastic pass but he needs the movement and Cengiz Under's quality for Vardy was a brilliant move and a brilliant goal.
"That is why he is a big player, he makes the big contributions in the big games, that shows you the level he is at and he is a world class player. I am lucky to have him ere.
"We deserved it, we played against a really good side and have players who can run in behind. To keep a clean sheet and play with the quality and calmness was good."