"This will never happen again," Munoz told ABC News' "Good Morning America" in an exclusive interview."We are not going to put a law enforcement official onto a plane to take them off … to remove a booked, paid, seated passenger. We can't do that."
The airline later announced that it would compensate everyone on board the flight for the full price of their ticket.
Regarding blowback Munoz received for his initial muted response, which did not include an apology, he said a more forceful reaction was delayed because he was still gathering the facts.
"I think my reaction to most issues is to get the facts and circumstances," he said. "My initial words fell short of truly expressing the shame."
Munoz said the feelings of embarrassment were "palpable" for him and his United colleagues.
The passenger, David Dao of Elizabethtown, Kentucky, a 69-year-old physician specializing in pulmonary disease, is at a Chicago hospital undergoing treatment for his injuries, according to lawyers for his family.
United Flight 3411, operated by Republic Airways, was set to depart Chicago's O'Hare International Airport at 5:40 p.m. local time Sunday, bound for Louisville International Airport, when the incident occurred.
United told ABC News that passengers were offered up to $800 to give up their seats for four members of a crew who needed to board. When no one volunteered, the airline generated a list of four names to be removed from the flight and be reaccommodated, in accordance with the airline's contract of carriage.
Of the four passengers, Dao was the only one who refused to comply, which triggered a call to airport police.
One of the officers involved was placed on leave Monday. The Chicago Department of Aviation said that it did not condone the officer's actions and that they were not in keeping with standard operating procedure.
"The aviation security officer in question is on paid administrative duty, pending an investigation," a department spokesman said Tuesday.
"It was a system failure," Munoz said. "We have not provided our frontline supervisors and managers and individuals with the proper procedures that would allow them to use their common sense.
"They all have an incredible amount of common sense, and this issue could have been solved by that," he added. "This is on me. I have to fix that, and I think that's something we can do."
Many social media users have called for a boycott of the airline.
The Rainbow PUSH Coalition, led by veteran politician and activist Rev. Jesse Jackson, has organized a protest for this afternoon at O'Hare airport in Chicago.
ABC News' Rebecca Jarvis, Whitney Lloyd, and Paul Blake contributed to this report.