In response to star striker and club captain Robin van Persie's decision to not extend his contract with the club, Usmanov said in an open letter to the Gunners' board that the club's current business model was geared towards making personal fortunes.
But Hill-Wood, who sold his shares to majority owner Stan Kroenke, has rejected these claims as "complete and utter rubbish" and believes the 58-year-old is threatening to destabilise the club.
He told The Guardian: "It was nice to make that money, but I was never involved in Arsenal for that reason.
"I was involved because I have been brought up to love Arsenal and that is my only concern.
"I do not know what he [Usmanov] is trying to do really, I don't think he is right."
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He continued: "We don't have the same oil wealth that [City's owner] Sheikh Mansour has. He is prepared to pay astronomical figures for players; we cannot pay that sort of money, and we can't compete."
Usmanov, however, believes that the board should pay off the stadium debt in order to ensure players like Van Persie can be retained but Hill-Wood disagrees.
"It's simple to say we should put some money in, but it doesn't make any sense," the 76-year-old said.
"We can't pay off the debt without huge penalties, and putting money in for any other reason doesn't make any sense at all.
"We give the manager as much money as we possibly can, and all we can do is continue. We have run the club sensibly, and we haven't done badly; it's not as if we have been relegated."