"We must do everything to clear racism so that there are no such incidents at any game," Platini told a joint news conference in Budapest with Hungarian Prime Minister Viktor Orban and Hungarian football association Chairman Sandor Csanyi.
Platini, speaking via a translator, said UEFA had decided to ban players or coaches making racist comments for at least 10 games, adding that stadiums where such incidents recur could be closed for good.
Platini declined to comment about a remark made by FIFA president Sepp Blatter on Monday that awarding the 2022 World Cup to Qatar may well have been "a mistake".
Csanyi said Hungary would be making a bid to be one of the host venues for the 2020 European Championship.
- Sports & Recreation