There have been a number of high-profile incidents of racism in the last 18 months and there was fresh debate about the issue when AC Milan midfielder Kevin-Prince Boateng and his team-mates recently walked off the pitch during a friendly after receiving abuse from the terraces.
Blatter reiterated his view that other players should not follow Boateng's lead by leaving the field, but he did repeat previous pledges to remove racism from the sport.
FIFA last week ordered the Bulgarian and Hungarian football associations to play a game behind closed doors in response to racist incidents and Blatter believes this punishment should serve as a warning that severe action will be taken.
During a Special Report interview with Sky Sports News, Blatter said: "I think we can never do enough to eradicate all the racism in football.
"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."
Asked for his thoughts about Boateng, he said: "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.
"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."
Blatter suggested he will call a "summit" of football's leaders in a bid to find a long-term solution, but did add that players found guilty of racial offences should "be suspended for more than one or two matches".
The 76-year-old plans to step down in 2015 and his last major event as head of the game will be next year's World Cup in Brazil.
England are currently qualifying for that tournament and Blatter insists that too many overseas players are harming the national team's chances.
"You have too many foreigners and not English players, so your national team is not yet, I have to say, is not yet at the level of these national teams I just mentioned," he said.
"If you look to Spain, Italy and Germany you realise that 80% or even more of the players of national team, they play in their own league, and so it is an influence of how many good players you have in your own league for the national team."