Nigeria scored the decisive goal eight minutes later through Peter Odemwingie.
Yesterday, long-time friend and fellow football referee Brett Chibnall defended Mr O'Leary.
"Things happen so, so quickly, it's unbelievable. I think [Mr Rule] had a really outstanding game. These things happen. Sport is played by humans, and if you put technology into the sport you might as well take the humans out."
Mr Chibnall said he thought Mr O'Leary, who is the head science teacher at Whangarei's Tikipunga High School, was correct to dismiss Bosnian complaints that there was a foul in the lead-up to Nigeria's goal.
"Basically it is a contact sport and the player was too easily outmuscled. I think you have to be strong."
He was hopeful the Kiwi team would be awarded control of another match at the tournament.
World Cup facts
Top scorer:
Karim Benzema, France, 3
Thomas Mueller, Germany, 3
Robin Van Persie, Netherlands, 3
Arjen Robben, Netherlands, 3
Enner Valencia, Ecuador, 3
Top runner: Serge Aurier, Ivory Coast, 19,342m
Top saves: Vincent Enyeama, Nigeria, 8 saves, 0 goals conceded.
Goals per match: 2.9
Matches played: 29/64
Source: Fifa.com