Lowy says Australia's $46-million bid, which received just one vote of support in a process unexpectedly won by Qatar, was clean of bribes and corruption but never stood a chance of winning.
"I have nightmares about all the work we did. And we didn't get anywhere," Lowy told Sky News in an interview broadcast on Tuesday.
"You just got to get on with it. I take the responsibility and I take the blame. I should have known better.
"Had I known that we had less than 50 per cent of a chance, I probably wouldn't have been there."
The bidding process for the 2018 and 2022 World Cups is being freshly investigated by Swiss authorities amid a wider corruption scandal enveloping soccer's world governing body, FIFA.
FIFA president Sepp Blatter will stand down from his role, despite winning re-election at a FIFA congress.
Seven FIFA officials were arrested in a dawn raid a Zurich hotel before the congress, part of 14 people charged by United States authorities.
The US allege the 14 people - current and former FIFA officials and sports marketeers - conspired to solicit and receive more than $US150 million ($A194 million) in bribes and kickbacks, in exchange for their support of marketing executives who agreed to make the illegal payments.
US authorities say those charged face up to 20 years in jail if found guilty.
One of the arrested men, Jack Warner, is alleged to have stolen $500,000 from Australia's bid.
Warner, the chief of the north and central American football association CONCACAF, has denied any wrongdoing.
Lowy said last week in a statement the Australian money was paid to CONCACAF but was ultimately found that Warner "had committed fraud and misappropriated the funds - in other words he had stolen the money from CONCACAF".
In his interview with Sky News, Lowy said he would cooperate with a flagged Senate inquiry and possible Australian Federal Police investigation into the failed bid.
"There were no bribes in this process," Lowy said.
He said the Australian money paid to Warner was not part of a corrupt process.
"I have no concerns about that," Lowy said. "The money wasn't sent or given to Warner, it was a cheque transferred to CONCACAF.
"Today is a major event because it was found out that Warner pocketed that money. But he took that money not from us, but took the money away from CONCACAF.
"I became aware a year, maybe 18 months, after the event, that he pocketed that money."
Lowy said Australia was trying to claim the money back from CONCACAF but "I don't know whether we are going to get it back".
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