"We're prepared to make some short-term sacrifices for the long-term gain of the sport," Brown told reporters at the Austrian Grand Prix.
"While I don't think we need to go to a flat revenue structure, clearly it is too out of balance compared to other sports and that's why we have this out of balance race results."
Mercedes, Ferrari and Red Bull are the only teams to have won Formula One races since Lotus triumphed in Australia in March 2013.
Brown said he aimed to "put Formula One first and McLaren a really close second", and smiled when asked whether all the other teams shared his view: "I doubt it."
Ferrari, champions Mercedes, McLaren and Red Bull currently receive special annual payments to reflect past success and their importance to the sport. Williams also get a smaller 'heritage' payment.
Ferrari, the only team to have been in the championship since it started in 1950 and the most successful, get a special long-standing bonus of around $68 million.
McLaren, still the sport's second most successful team despite not having won a race since 2012, finished sixth overall in 2016.
However, projected figures published by autosport.com in May showed they stand to be paid $97 million in 2017 compared to the $72 million that Force India will receive for finishing fourth.
That still pales in comparison to the $180 million paid to Ferrari and $171 million going to champions Mercedes. At the end of the scale, newcomers Haas will get only $19 million, according to Autosport.
Formula One's underlying revenues are estimated at $1.38 billion, with the teams sharing roughly 68 percent.
"This is a time where I think we need to work together to grow the sport," said Brown, whose Honda-powered team are last in the current standings and have Bahrain's holding company Mumtalakat as a major shareholder.
"I’ve been asked questions on 'do you think you get the right slice of the pie?’ 68 percent now. Of course I’d love us to have 75 and I’m sure (F1 owners) Liberty would love to have maybe 55.
"I think the percentage is less relevant if we can double, triple our group or the size of the pool."
Liberty Media, who completed their takeover of Formula One in January, have said they want to rebalance revenue payments once commercial agreements with teams expire in 2020.
"We've got tracks going bust, we have teams going bust and then some people getting really rich. The poor guys need to at least be able to make a living," said Brown.
"We need to get that water pipe up to where at least if you are at the back of the grid you can make a living and your franchise is worth something and you have the opportunity to move forward.
"I think it would be great to have an underdog team win a couple of times a year."
(Editing by Amlan Chakraborty)
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