Blatter, in an hour-long interview on BBC Radio Five Live on Thursday, said he thought financial penalties for offenders were inappropriate because there was too much money in football and fines are easily paid.
"There must be a sporting sanction (against offenders)," he said. "It is about points, they must lose points.
"Also the match should be stopped and those who have been racist should be identified by the surveillance and kicked out of the ground."
Blatter added that FIFA took a tough stance against racism but said the 45,000 pounds ($78,670) fine handed out to the Spanish FA after home fans racially taunted England players in a friendly in a Madrid a year ago was not enough.
"It was easy for them," he said, "there is too much money in football."
However, Blatter said teams would not be deducted points if there was racism at the World Cup finals in Germany next year.
BAD FANS
"The World Cup is a competition held over a very short period, it is not a league programme of 40 or 42 matches," he said. "Also it is a knockout competition and it would be very dangerous to have that system in the World Cup.
"Bad fans could organise racism, it is not practical to deduct points at the World Cup, we have to find a middle ground."
He also said FIFA's monthly world rankings system would provide the basis of seeding for the World Cup draw in December but that other factors would also influence the outcome.
The World Cup organising committee will decide on the seeds at a meeting in Leipzig on December 6, three days before the draw.
In an article in Britain's Financial Times on Wednesday, Blatter accused the owners of the world's richest clubs of creating a "Wild West-style of capitalism" that threatens to kill the game.
Blatter said FIFA were setting up a task force to examine the "pornographic amounts of money" that have created big divisions in the sport.
"More than ever before, the majority is fighting with spears, while the greedy few have the financial equivalent of nuclear warheads," he wrote in his occasional column in the newspaper.
He returned to that subject on Thursday, saying the vast amount of money poured into several rich clubs was destroying the "solidarity of football".
