As the globe's most popular sport, the iconic former France international said, football has a particular role to play in confronting prejudice.
"Football is honour-bound, by virtue of that very popularity, to promote values which are able to make society more tolerant of diversity," Platini told campaigners and diplomats at a session on racism and sport at the UN's offices in Geneva.
Over recent years, UEFA and its global football counterpart FIFA have increased the severity and number of punishments able to be imposed for racist offences.
Among them are fines and ordering matches to be played behind closed doors, while referees have the power, albeit little-used, to halt games marred by racist chanting.
There have been mixed opinions among football chiefs, however, about whether players should take matters into their own hands.
The prime example came when Ghana international Kevin-Prince Boateng stormed off the pitch in January during a friendly between his then club AC Milan and a lower-league Italian side.
While UEFA's leaders backed him right away, FIFA boss Sepp Blatter initially cast doubt on such unilateral action, before finally swinging behind Boateng.
"Those who govern our game have a duty to protect players, who are in their workplace, against all forms of discrimination," Platini said.
In May, FIFA created an anti-racism taskforce headed by Jeffrey Webb, who is also boss of the North and Central American and Caribbean football federation, CONCACAF.
"The FIFA anti-discrimination taskforce is committed to eliminating racism on and off the pitch," Webb told the UN meeting in a video address.
But with high-profile cases continuing to hit the headlines — most recently in Great Britain, Italy and Ukraine — campaigners argue that more effort is needed.
"There's a real problem with racism in some regions of Europe, for sure," said Platini.
"This behaviour is largely down to small organised groups who choose to express their hatred in a football stadium in order to take advantage of the popularity and media coverage enjoyed by our sport."
But the broader context could not be ignored, he said.
"Football reflects society's values but also, unfortunately, its prejudices, fears and mistrust," he said.
"But it's precisely because football is often more open to diversity than wider society that it enables advance that would be more difficult in other areas."
Hand-in-hand with sanctions, football bodies have run repeated anti-racism campaigns to try to change attitudes, working with activists, governments and international organizations.
"Racism is not a problem of football," said Wilfried Lemke, the ex-chairman of German club Werder Bremen who advises UN Secretary-General Ban Ki-moon on sport's role in peace and development.
"Racism is a problem of society, of people, of governments, of schools, of homes and neighbourhoods," Lemke said.
"UEFA and FIFA have done a lot, and I think we cannot ask for more and more that could be done by the sport entities. Let us try to check what governments, very concretely, are doing," he said.
"Zero tolerance on the pitch and off the pitch, that's very, very important."
FIFA's taskforce members include Tokyo Sexwale of South Africa -- where the former apartheid regime was hit by an international sporting boycott and where sport has been a touchstone for national unity since its fall.
Sexwale, who was in prison along with former South African president Nelson Mandela, recalled his mentor's words on the strength of sport.
"It is more powerful than governments in breaking down barriers," he said.