Patrick, 26, has her racing goggles focused on the Indianapolis 500 instead of following Castroneves to Dancing with the Stars fame.
"I can dance, since I was a cheerleader," Patrick tells PEOPLE. "But I don't have the personality that Helio does; he won everyone's heart. I would be a bit too serious for the show."
Castroneves, last season's Dancing champ, fell short behind the wheel at the Japan 300, but he was graceful in defeat to the woman who bested him.
Helio: 'I'm Happy for Her'"My hat is off to her. Yes, I'm disappointed that I wasn't able to take the victory, but this is great for the series," Castroneves tells PEOPLE by e-mail. "She's a talented driver. It can take an experienced driver several seasons to win a race. I think it's great and I'm happy for her."
The landmark, Patrick says, was an emotional experience.
"It didn't hit home until I crossed the finish line," she says. "I thought: 'Holy crap, I finally did it.' I got emotional and started to cry. All I could say over the radio (back to my crew) was 'Thank you.'"
The go-faster gal feels no need to put her foot down when misguided males disparage her achievements on the circuit.
"They've never made me mad, I think they're funny." she laughs. "I take all their comments as just jokes. I mean, I make jokes about women drivers, too."
"I think anyone in any profession has to deal with people who don't believe in them – even though I've given plenty of reasons for people to believe in me," Patrick adds. "So, this isn't about girls versus guys, it's about believing versus not believing."