Garner explained to Radio Live that though consent forms were signed and that people were instructed not to jump up while on camera and that everything went fine during the first two rehearsals, there was a "genuine mistake" when it came time for the live TV cross.
Touching on the matter on his Radio Live show Garner said the accidental flashing was "not a laughing matter."
"It was a genuine mistake. It shouldn't have [happened], which is why we apologised."
Garner also admitted that the Story team were "always a bit worried" that something like that would happen but said that "It was only a fleeting moment."
"We're sorry," he said, "Hopefully it's not the end of the world. I hope it didn't offend too many people."
The show almost predicted the faux pas by tweeting about the segment before it aired with the hashtag #SoMuchCouldGoWrong.
The close-up exposure comes on the same day as MediaWorks - the company behind TV3 - chief executive Mark Weldon announced he was stepping down after a controversial tenure.