Vichai Srivaddhanaprabha and four other people were killed in the crash outside King Power Stadium on October 27, BBC Sport reported.
Today’s Premier League match in Cardiff is the Foxes' first since the incident and manager Claude Puel said the result is "not important".
But Vardy said, "For us as players, we want to get a positive result."
Speaking to Sky Sports, the 31-year-old added, "We need to make sure we go out there and honor his name and put in a performance that will hopefully get the win.
"We all spoke about wanting to play. It's what Vichai would have wanted and that's what we are going to do.
"It's going to be tough and very emotional and what the lads wanted to do was play this game and honor the man himself."
All Premier League games this weekend will be preceded by a minute's silence, and players will wear black armbands.
Srivaddhanaprabha's funeral will begin in his native Thailand today and could last a week. Puel said players would be given the opportunity to attend.
"It's been the hardest week of everyone's lives," said Vardy. "It'll be massively important we attend. We are a close-knit group and one big family and one of the main reasons for that is Vichai – so it's massively important.
"He wasn't just a chairman, he literally was part of your extended family."