"The offside, in hindsight, wasn't offside so it should have been a goal. But it was the call of the referee's assistant (Mark Rule) and unless the referee sees differently, he has to go with the judgment of his assistant," Mr Alabaster said.
"And with the supposed free kick; I've looked at it a number of times ... It wasn't a free kick, as the Bosnia player just fell over. There's way too much of that falling over whenever somebody touches you so really that's what you deserve when you go down so easily.
"Peter likes to keep the game flowing and he's a very, very good referee. In fact I'd say he's probably the best New Zealand referee I've ever seen."
Mr Alabaster said he wasn't really surprised by the vitriol directed toward Mr O'Leary, however misguided it may be.
"Kiwis don't really understand how much football means to some of these nations. We are passionate about our rugby, but that's nothing compared to football to these people. It means everything to them. A country's economy can rise or fall depending on how well their football team is going."
Read more: 20,000 sign petition against Kiwi ref
Within hours of the game a nasty call from somewhere in Europe was left on the Northern Advocate's editorial line making threats to kill Mr O'Leary. It was purportedly from a Bosnia and Herzegovina fan.
Details of the call have been passed on to Whangarei police, who are investigating. The teams were scoreless early in the match when Bosnia-Herzegovina striker Edin Dzeko scored.
Replays showed Dzeko to be onside by at least a step, but Mr O'Leary's Kiwi assistant, Mr Rule, raised his flag for the offside and the goal was disallowed.
Shortly afterwards, Nigeria's Peter Odemwingie scored, but Bosnia and Herzegovina players said he had fouled a defender.
The other Kiwi assistant referee, Jan-Hendrik Hintz, ruled it a fair challenge and the goal stood, leaving Nigeria to win 1-0 and putting Bosnia and Herzegovina out of the tournament.
An online petition calling for Mr O'Leary to be sacked by Fifa on change.org has been signed more than 23,000 times by online users.
Shortly after the 1994 World Cup, Colombian defender Andrs Escobar was shot and killed for scoring an own goal in a match against the US that put Colombia out.
It is unclear whether Mr O'Leary and his assistants will feature in any more matches.
Refereeing appointments are made two days before games, with Cup performances taken into account, and the Kiwis have not been appointed to any of the next five games.
Petition - Fire Peter O' Leary from his Referee job and change result on Bosnia-Herzegovina v Nigeria to 1 v 1.
