The Foxes came from 3-1 down to clinch a 5-3 victory at the King Power Stadium, with Vardy scoring the goal that put Leicester ahead for the first time.
The striker told At The Races: "The fans were amazing and the players were amazing. It's not about me scoring, it's about the team winning, and that's all that matters.
"We haven't had the easiest starts to the season, but we've already shown what we are all about. It's on to the next game now and trying to get three points."
The result leaves Leicester seventh in the Premier League table.