Doherty wrote the letter after "ESPN: The Magazine" published a column revealing that Doherty told his players that Duke "still has the ugliest cheerleaders in the ACC."
The comment was made in a team huddle late in the second half of the hotly contested game.
But UNC sports officials and Duke student leaders both say the comment has not caused an uproar.
"I said it as a joke to lighten the obvious tension my players were feeling during the game against Duke," Doherty wrote in the letter. "However, I apologize for the insensitive reference and hope you did not take it seriously or personally."
Steve Kirschner, UNC director of athletic communications, said the comment became public after a team member told a friend what Doherty had said.