Parrott was crew chief for the No. 43 car driven by Aric Almirola for the last year. NASCAR suspended him indefinitely last week for failing a random drug test.
Petty said there was no way to keep Parrott with the team following the failed test.
"Circumstances beyond our control," Petty said Tuesday during an appearance at the NASCAR Hall of Fame. "It was just an automatic. What he did was what he did. All we did was say, 'This is the way it's going to be.' It's definitely zero tolerance. These guys (the drivers) are putting their life on the line, the guys on pit road are putting their life on the line, so 100 percent ain't good enough, OK?"
Parrott, the former crew chief for Hall of Fame driver Dale Jarrett, told Eli Gold on Motor Racing Network's "NASCAR Live" that he made a mistake. He would not reveal the substance he took in the Tuesday night interview with Gold.
"I was in a dark moment, and it happened," the 49-year said. "The next morning when I woke up, I just couldn't believe what I'd done and beat myself up pretty bad about it. I had to go face the truth."
Parrott, who led Jarrett to the 1999 Cup championship, two Daytona 500 wins and two Brickyard 400 wins among his 31 victories, said he'll start NASCAR's "Road to Recovery" on Wednesday.
"I'm going to get the problem fixed and make sure that something like this never happens again," Parrott said. "I love this sport. I want to get back in this sport and work with my friends in the garage area."
Almirola said he spoke with Parrott following the NASCAR suspension.
"I just reached out to him and told him I supported him, I just wanted him to get better and get back on track," Almirola said. "I don't know what else to say to the guy. I've said it over and over, this isn't a character flaw. He's still a good person and a good crew chief, but he made a mistake and now he's got to bounce back."
Car chief Greg Ebert was elevated to interim crew chief beginning with this weekend's race at Martinsville Speedway. Ebert has been Almirola's car chief for the past two years. He previously spent five seasons as car chief for Matt Kenseth at Roush Fenway Racing.
"I think it's going to be pretty seamless," Almirola said. "Greg's been the one guy who has been around the car a lot. He's the one guy who has been up to speed with the setup stuff that has evolved throughout the year. He's obviously in a leadership role already, so it was natural to move him up."