Brown spoke out after 18-year-old winger Ryan Fraser rejected a contract offer and indicated his desire to move on after playing just two full games for the club.
Aberdeen have already lost Scotland Under-19 defender Jack Grimmer and Scotland Under-21 international Fraser Fyvie this year. Grimmer left for Fulham for a reported fee of £200,000 and 19-year-old Fyvie signed for Wigan in the summer after refusing to extend his contract beyond December.
Last year Scotland international Chris Maguire signed for Derby on expiry of his contract with the clubs agreeing a fee to prevent a FIFA tribunal. And Brown believes the cost of young Scottish talent is far too cheap for cash-rich English clubs.
"It will happen again for sure," said Brown, whose team face Motherwell in a William Hill Scottish Cup fifth round replay at Fir Park on Tuesday night.
"If we could stop it happening we would stop it. My decision to stop it is at FIFA level. The compensation should be far, far more.
"The English clubs can take a gamble on them and make the boys starry-eyed with a bigger wage. If they had to pay compensation commensurate to a transfer fee it would act as a bit of a deterrent.
"It wouldn't stop them because, I keep saying this on Celtic's behalf, it's an uneven playing field in Europe.
"They get a couple of million from television and the top clubs in the English Premier League get £67million.
"If they have £67million from television they can gamble a couple of quid on a young player. If compensation was higher they would maybe think twice and we would get commensurate recompense to the work we put into that boy."