"We ran a clean bid. I know that others did not, and I have shared what I know with the authorities, including Michael Garcia who undertook a two-year investigation into the 2022 World Cup bid," he said in an open letter.
Australia was vying to host the 2022 tournament, which was controversially awarded to Qatar, along with the United States, Japan and South Korea.
Australia secured only one vote despite ploughing more than Aus 40 million (USD 31 million) into the bid and Lowy, the founder and head of global shopping centre empire Westfield, said it left a bitter taste.
"We ran a clean bid and we are proud of that but it wasn't a level playing field and therefore we didn't win it. I will always be bitterly disappointed about the outcome."
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His comments come with FIFA embroiled in two separate investigations by American and Swiss authorities into alleged rampant and long-running corruption within the organisation.
Several top FIFA officials were arrested in dawn raids in Zurich last week and accused by US investigators of taking tens of millions of dollars in bribes, while Sepp Blatter announced his resignation on Tuesday just days after being re-elected to a fifth term as FIFA president.
Australia broke ranks with the Asian Football Confederation last week to vote against Blatter, to whom Lowy had been a long-time ally, and the mogul said recent events had been a watershed moment for the world sporting body.
"Sepp Blatter's resignation should open the door to major reform," he said.
"I say should because FIFA's problems are deep-rooted and tangled in a culture that has developed over decades. It will take a united, concerted effort by its football associations to fix the mess.