The push for tougher anti-racism sanctions was revealed late Saturday by Blatter in a speech in England, days after the Manchester City team was subjected to racial abuse in Russia, which is hosting the 2018 World Cup.
CSKA Moscow is facing UEFA disciplinary action for its fans' abuse on Wednesday of City midfielder Yaya Toure, with a partial stadium closure for the Russian capital club's next European match the likely punishment.
But Blatter believes the sanctions championed by UEFA President Michel Platini are not strong enough, saying just banning fans from stadiums, or fining national associations or teams is not the solution to eradicating racism from football.
"It has been decided by the FIFA Congress that it is a nonsense for racism to be dealt with, with fines, you can always find money from somebody to pay them," Blatter told a gala dinner celebrating the 150th anniversary of the English Football Association. "It is a nonsense to have matches played without spectators because it is against the spirit of football and against the visiting team, it is all nonsense.
"What we shall do is be very tough, we need to eliminate teams from a competition or deduct points. Only by such decisions is it possible to go against racism and discrimination. If we don't do that it will go on and go on. We have to stop it. We need the courage to do it."
The head of FIFA's anti-racism task force, FIFA vice-president Jeffrey Webb, plans to meet Toure on Sunday at Stamford Bridge when City plays Chelsea.
The FIFA Congress in May approved much tougher penalties for serious racist abuse, including point deductions and relegation.
"We can do something better to fight racism and discrimination," Blatter said Saturday. "This is one of the villains we have today in our game but I'm sure, with the combined efforts of everybody we can go on, but it is only with harsh sanctions that racism and discrimination can be washed out of football."
Speaking on the site of the English FA's first meeting in 1863, Blatter praised the world's oldest national football association for creating the "perfect" environment for matches by eradicating the hooliganism and racism that once blighted the game here.
FA President Prince William, the second in line to the British throne, told the dinner that there is "sadly more work to do" still to combat racism in football.
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