Racism was thrust back into the spotlight when AC Milan midfielder Kevin-Prince Boateng led his team mates off the field during a friendly against Italian fourth-tier side Pro Patria earlier this month after suffering abuse from fans on the terraces.
Pro Patria were ordered to play their next home match behind closed doors because of their fans' behaviour but Blatter suggested racism might warrant greater punishment.
"I think a more radical solution would be deduction of points," Blatter told Sky Sports News.
"Deduction of points would have a better impact on that (racism) than any other sanction."
Blatter, who had to clarify 2011 comments denying racism was a problem in football and that incidents could be settled with a handshake, praised Boateng for showing courage in walking off but said it was not a long-term fix.
"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," the Swiss said.
"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 had promised to tackle the 'devil' of racism in what he says will be his final four-year term as the head of the sport's world governing body, but despite his efforts the high profile cases keep coming.
Last week FIFA ordered Bulgaria and Hungary to play World Cup qualifiers behind closed doors because of racism, with European body UEFA handing out fines to Serbia and clubs Porto and Lazio in other recent cases.
"I think we can never do enough to eradicate all the racism in football," Blatter said.