"I really couldn't make up my mind, so I had to do it the honest way," the pass-rusher told reporters on his introductory conference call, according to Chris Emma of 670 The Score. "The Bears were on the right side."
Quinn agreed to a five-year, $70-million contract with Chicago on March 17, the second day of the NFL's legal tampering period.
"That's kind of how it came down to the final decision," Quinn said. "It was still pretty tough. I mean basically that's what it boiled down to is a coin flip. I don't regret it."
The Bears later refuted Quinn's claim.
Quinn posted 11.5 sacks in 14 games for the Dallas Cowboys in 2019, a spike from the 6.5 sacks he notched for the Miami Dolphins a year earlier.
The Falcons, meanwhile, went after Dante Fowler after losing the supposed coin toss, signing the former Los Angeles Rams edge defender to a three-year contract worth $48 million.