The Fifa president claims he has found the best method of eradicating discrimination from the game, and has criticised Kevin-Prince Boateng's recent walk-off protest
The issue of discrimination was brought to the fore again when Milan players walked from the pitch during a recent friendly clash with Pro Patria after Kevin-Prince Boateng suffered racial abuse.
And the 76-year-old head of the world's football governing body has offered what he claims is a "radical solution" to such behaviour.
"I think we can never do enough to eradicate all the racism in football," Blatter told Sky Sports.
"We have already tried and you have given, in Great Britain, the best example of how to eradicate violence in football with the modern stadia, with the controls and education that this is the one thing.
"I think a more radical solution would be deduction of points. Deduction of points would have a better impact on that than any other sanction."
Blatter also moved to discourage a repeat of Boateng's protest, describing taking such action as "running away" from the problem.
"Already to have a match played without spectators is a warning, it's a warning for all the spectators but the situation is now as such, you remember the Boateng problem, running away," he added.
"I made a comment on that and I still have the same feeling, it was good what he has done in order to give this impact by saying 'listen, look at what has happened' but it can't be the solution.
"It can't be the solution because you can never solve any problem in your life, being in private life, in economic life, wherever, by running away.
"This is a good sign, it's a good sign, to now say listen, if you don't take care now of our sport they will do it."