A BBC Panorama programme highlighted racism incidents at grounds in Poland and Ukraine, who co-host Euro 2012.
Manchester City and Italy striker Mario Balotelli threatened to walk off the pitch if he believed he was a victim.
But Platini said: “It’s a yellow card. It’s not a player – Mr Balotelli – who’s in charge of refereeing.”
Platini insists officials will deal with any racist incidents that occur during the tournament, which begins on Friday.
“It’s the referee who takes these decisions. Referees can finish the game. They have this power in case of racism,” Platini told the BBC sports editor David Bond.
“That is, I think, the best way to protect the game against racism.
“The referee has been given advice and he can stop the game if there are problems.”
But both Premier League referees’ chief Mike Riley and executive director of Football Against Racism in Europe, Piara Powar, say the situation should not arise.
Piara said: “[Euro 2012 Respect ambassador Pierluigi] Collina was clear that if a player did approach a referee and was looking for help, that the referee would then facilitate the player leaving the field of play.
Platini dismissed suggestions his reputation would be tarnished if there is racial abuse at Euro 2012.
“Are you joking? You think I am responsible for the racists in the rest of Europe or in England or in France?” he said.
Platini said Uefa had done a lot to tackle racisim, backing such initiatives as ‘Never Again’, but said he was “not responsible for society”.
He added: “Society is not so easy. You have some problems and we have to organise these Euros from the beginning with some problems because these two countries never welcome so big an event in the past.
Bond meets Platini
“Over the next month Ukraine and Poland will be in the spotlight in a way they have never encountered before. Should it go wrong then the reputation of Uefa and its ambitious French president will also be on the line.”
“It was a big challenge for Poland, big challenge for Ukraine, a big challenge for Uefa, and we have done our best.”
Asked about the footage shown in Panorama’s documentary, Platini said: “We are shocked about racists but we are trying to do something; we have to fight against that.
“I feel bad. Of course I feel bad because I am not a racist.”
The 56-year-old former France international midfiedler also insisted the issue of racism is one that extends far beyond the two host nations of Euro 2012.
Platini, who has been Uefa president since January 2007, said: “If you want to have a programme on racism you can go everywhere now because there is an increase in the nationalists in many, many countries.
“It is not just a fact only in Poland and Ukraine.
“You can go in France, United States, in England and you will find the problem of racism.
“You have more nationalists in many, many countries in east of Europe – that is true.”
The Uefa president has previously criticised the host nations, describing Ukrainian hoteliers as “bandits” for the rising cost of accommodation and bemoaning the quality of pitches in Poland.
The Ukrainian president, Viktor Yanukovych,has downplayed fears over racist attacks in Ukraine, saying hooligans were known to the authorities and security services “will be watching all the matches closely”.