The R&A announced minimal increases to prize money for the 152nd British Open this week amid "concern" about the impact on financial sustainability and the perception of men's golf.
The winner at Royal Troon on Sunday will receive £2.38 million ($3.1 million), which is an increase of just $100,000.
Bryson DeChambeau earned $4.3 million for winning last month's US Open, while Scottie Scheffler's Masters victory in April came with a $3.6 million prize.
The total British Open prize fund of $17 million is up by just $500,000 on last year and stands as less than the other three majors, 12 PGA Tour events and all 14 LIV Golf events.
"A, I didn't know, and B, I don't care," said Slumbers, who is set to step down from his role in November.
"While we will always offer a very competitive prize fund for the Open, our wider focus is on increasing participation and improving pathways in golf.
"We have to make choices about how we allocate resources and make the resources we have go as far as they can. Our responsibility is to ensure the game is thriving 50 years from now.
"I'm not worried about being a lone voice. Sometimes leadership is lonely."
A total of 158 players, rather than the usual 156, will contest this year's British Open after more past champions than expected opted to play at Royal Troon, with 18 players from LIV Golf in the field.
But while USGA chief executive Mike Whan said last month he is serious about creating a formal pathway for LIV players into the US Open, Slumbers suggested that was not necessary for the British Open.
"We decided after last year's event that we wanted to ensure that there was sufficient enough opportunities for all players, whichever tour they're playing on, to get into the Open," he said.
"We used our Open Qualifying Series. We picked events that were available for all players. We used the Asian Tour and we used final qualifying to create those opportunities.
"Will that evolve in the coming years? I think that depends on how the game evolves. But we will continue to want the best players in the world to be able to get into the Open in an appropriate way."
As for future venues, Slumbers said that the Open was "absolutely" going to return to Muirfield for the first time since 2013.
The possibility of staging the Open outside the UK for the first time also remains on the agenda, with Portmarnock having asked the Irish government for support in putting forward a case to stage the event.
"We are fully supportive of the club doing that and we are actively engaged in making those assessments," Slumbers said.
"But no decisions have been made because we don't even know if it's possible."
