The issue has come under the spotlight in recent weeks due to incidents involving Dani Alves of Barcelona and Milan's Kevin Constant, who each had bananas thrown at them from the crowd in games at Villarreal and Atalanta respectively.
Villarreal and Atalanta have since been punished, with the Spanish side fined €12,000 and the latter docked €40,000 and ordered to close their Curva Nord section for one game, although the second sanction has been suspended for one year.
The UEFA congress agreed last year that all incidents of racism must be punished by partial stadium closure for a first occurrence, and by full stadium closure and a fine of €50,000 for a second such offence by supporters.
And Platini has urged UEFA's member associations to adhere to those guidelines.
"The UEFA Executive Committee strongly condemns all acts of discrimination and I was outraged by the incidents which took place in recent weeks," Platini said following separate meetings of the Executive Committee and Professional Football Strategy Council (PFSC) in Turin on Tuesday.
"It is unacceptable for anyone to be racially insulted or abused inside our stadiums, and we simply cannot tolerate it.
"We call on all our member associations and stakeholders to apply a zero-tolerance policy against all forms of discrimination and to follow the UEFA guidelines in sanctioning all guilty parties.
"Our statutes were recently amended to ensure all UEFA member associations adopt effective policies to eradicate racism."
