The head of UEFA's governing body believes fans — not the teams they support — should be held accountable for their behavior.
Clubs found guilty of racist abuse from their supporters can incur a fine and be forced to close a section of their stadium by UEFA, but Platini believes those responsible should be targeted instead.
"You can’t punish players, officials, clubs for something that they didn’t do," the Frenchman said during a visit to Moscow. "You have to punish the spectators. We've discussed this problem at the UEFA congress. If one footballer abuses the other he's banned for the offense. But for the unruly behaviour of fans we have to penalize the spectators.
"We had and will always have zero tolerance to racism. You can close the stadiums partially or completely in case of the fans' racist behavior."
CSKA Moscow was the latest side to receive sanctions after a section of its supporters was found guilty of racist chanting aimed at Manchester City's Yaya Toure during a Champions League clash in October.
The club will be forced to play in front of a reduced capacity when it faces Bayern Munich later this month.