Chiesa (14-3), whose rescheduled fight against Anthony Pettis takes place in Las Vegas at UFC 226 next weekend, sustained multiple cuts to his forehead after McGregor and his entourage smashed windows on a bus filled with fighters leaving a media event at the Barclays Center.
"I don't really have too many kind things to say to [McGregor]," Chiesa told reporters at a UFC 226 promotional event .
"I lost a title shot. I have proof. I was the highest ranked guy on the card, I would have stepped in to fight Khabib at the drop of a dime. I got f----- out of that opportunity."
McGregor recently said he regretted his actions when appearing in court in New York -- but Chiesa was not in a forgiving mood as he spoke to the press.
"You work your whole life for those kinds of opportunities," Chiesa added. "To lose that opportunity, man, that's tough. You know how this sport works, guys. Opportunities like that don't come along. I could string together 15 wins in a row and still not get a title shot.
"I lost my opportunity at my dream. And, I hope that I'm going to fight my ass off to earn it back starting on July 7 with Anthony Pettis. But yeah, tough, tough pill to swallow."
Chiesa had previously been silent on what happened back on April 7.
"This is the most I've said about it," he said. "I've tried to stay mostly closed off, but f--- it. You guys want some answers, you got some."
McGregor last fought in a UFC bout back in Nov. 2016, when he defeated Eddie Alvarez at New York's Madison Square Garden to win the promotion's lightweight belt.
He never defended the title, and opted to fight Floyd Mayweather Jr. last August in a conventional boxing match instead. McGregor's technical knockout defeat to Mayweather was the second biggest pay-per-view fight in history.
Information from Reuters was used in this report.