Ghana midfielder Kevin-Prince Boateng led his Milan teammates off Thursday during a friendly against lower division club Pro Patria following racist chanting by fans.
The match was abandoned, but Blatter does not believe walking off is the best way to combat racism.
"Walk off? No. I don't think that is the solution," Blatter was quoted as saying on the website of Abu Dhabi's The National newspaper on Sunday.
"I don't think you can run away, because eventually you can run away if you lose a match," he added. "This issue is a very touchy subject, but I repeat there is zero tolerance of racism in the stadium."
Blatter said FIFA is yet to receive a report into Thursday's incident from the Italian football federation, which has opened its own inquiry.
"The only solution is to be very harsh with the sanctions," Blatter said. "And the sanctions must be a deduction of points or something similar."
In response to Blatter's comments, Milan manager Massimiliano Allegri defended his team's actions.
"We wanted to give a signal. Players can't suspend a match but others can," Allegri said. "There need to be rules put in place. We made a signal for the future. There needs to be more civility in Italian stadiums."
After being targeted by repeated chants, Boateng picked up the ball and kicked it at a section of the crowd in the 26th minute of the match Thursday in Busto Arsizio, a town north of Milan. He then took off his shirt and walked off the field with his Milan teammates.
Italian police have already identified several perpetrators of the abuse and prosecutors are considering whether to press charges of inciting racial hatred against them.
Milan players wore anti-racism tops before a 2-0 win over Siena on Sunday.
On Saturday, there appeared to be racist boos from Lazio fans directed at Cagliari players, but the match was completed as usual.Suggest a correction