The 60-year-old, who was succeeded after seven years by businessman Greg Clarke on Friday, believes that the current financial model at league clubs outside of the Premier League is not sustainable.
"The business model of professional football in this country doesn't work, it's broke and you see that reflected in the administrations and all the rest of it," Mawhinney said.
Speaking to the BBC, Mawhinney said a salary cap throughout the Football League from Championship to League Two would halt spiralling debts.
"I have some clubs in the Football League who are paying up to 85 percent of their income in wages. I don't care how great you are, you may be the best business entrepreneur the country has ever come up with but you cannot run a sustainable business with that sort of model."
An increasing number of league clubs have fallen into administration in recent years, while many are laden with mounting debts.
Last week Championship side Cardiff City were given 56 days to pay off arrears of around 1.9 million pounds, and the problem is creeping into the Premier League with Portsmouth in administration with debts of around 78 million.
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