"I am supposed to be a role model and I can only apologise," he told Ulster Television.
"I can guarantee from my point of view it will never happen again.
"It was one of those regrettable incidents that somebody said something and I made a silly gesture, which ultimately I regret."
Healy's agent Stephen Hughes explained what tempted the player into making the gesture: "David has told me he was wearing boots with a Northern Ireland flag on the back.
"The Celtic fans saw that and know he's a Rangers fan. They were chanting, 'Where were you on the 12th', which is the day of the Orange marching bands in Belfast.
"So he simply pretended to play the flute. There was no attempt to inflame the fans."