McGregor told ESPN that seeing a video of the April incident, which surfaced last week, was "like a dagger into my heart."
McGregor allegedly punched the man because he had twice refused a free shot the former fighter was offering patrons of his signature whiskey.
The 31-year-old called his behavior “unacceptable” and said the man deserved to enjoy his time at the bar “without having it end the way it did.”
He told ESPN he had apologized to the man at the time but added that he still needs to take “accountability” and “responsibility” for his actions.
“I owe it to the people that have been supporting me. I owe it to my mother, my father, my family. I owe it to the people who trained me in martial arts,” he said. “That's not who I am.”
McGregor was involved in another altercation in March when he was arrested in Florida for allegedly taking a man’s phone and smashing it on the ground. The criminal charges were later dismissed.
Authorities in Ireland are still investigating the incident.