Lewes - the only football club to pay their men's and women's teams equally - have asked the Football Association to address the "vast differences" in FA Cup prize money.
In an open letter, the club's directors point out the winners of the women's FA Cup collect £25,000, compared to the £3.6m given to the men's holders.
In addition, the total FA Cup prize fund for women's teams is £250,000 - less than 1% of the men's £30.25m.
"We could go on and on," Lewes said.
"If we are all really serious about rapidly driving huge positive change in the women's game then the FA Cup prize fund provides a powerful mechanism to do so. Let's use it.
"What a story it would be for the world's most beloved domestic cup competition to become the Holy Grail that champions women's football into a whole new era."
Prize money in the women's competition has tripled since 2015-16, yet the sum awarded to the winners of the men's FA Cup has doubled since the 2017 BBC Sport study into prize money in sport.
|Differences in FA Cup prize money|
|Total prize money (all rounds)||£30.25m||£250,000|
|Winners' prize money||£3.6m||£25,000|
|Fifth round winner||£360,000||£3,000|
|First round proper winner||£36,000||£850|
|Preliminary round winner||£2,890 (loser receives £960)||£325|
The open letter pointed to the fact teams stepping up to the FA Women's Championship - the second tier of women's football, in which Lewes play - requires a minimum of £100,000 per year - a sum "completely unattainable" for most clubs.
"Not because of some static and universal law that women's football attracts less attention and less revenue than men's football, but as a result of decade upon decade of negligible resources being made available to the women's game," the club said.
Lewes - who are ninth in the league - said they "applauded" the FA's focus on women's football but wanted to provide a "healthy challenge".
Chelsea are the current holders of both the men's and women's FA Cups.
"We know that you consider the FA Cup to be a good way to redistribute wealth to the grassroots in the men's game," the club said.
"That same FA Cup provides an ideal mechanism for financially irrigating the women's game. So we are suggesting a radical increase in the women's FA Cup prize fund.
"Let's get these prize funds to a level that we would all be able to tell our children about without embarrassment (try explaining the disparities in prize money to a child and you'll see what we mean).
"That would at a stroke increase the level of focus and seriousness paid to the women's game by existing clubs by an order of magnitude."
An FA spokesperson said: "The prize fund for the 2018-19 Women's FA Cup is the largest in the history of the competition and over £252,000 will be distributed across the competing teams.
"Whilst we recognise there is currently a significant disparity between prize money for the men's and women's competitions, these are determined by the amounts of money generated through commercial revenue, including national and international broadcast rights.
"The FA Cup is the biggest revenue producer for the FA and currently generates £212m per annum. This revenue enables us to invest back into football at all levels and we have made significant progress to develop the women's game as a result.
"We have invested over £18m into the 'Game Plan for Growth'; our ambitious strategy for the women's game, which plans to double participation, deliver professional and semi-professional women's football and a successful England team.
"We are also currently developing a five-year strategy with the FA Women's Super League and Championship clubs to grow audiences and revenues, which will help make women's football in England more commercially viable in the future and allow further re-investment."