The former France captain wrote in the latest edition of the European ruling body's newsletter that encouraging strides had been made to tackle bigotry and discrimination over the years.
But he added: "Appalling incidents continue to blight European stadiums from time to time, showing that the battle is far from won against a scourge that it is virtually impossible to wipe out completely."
In the English Premier League, for example, there have been a number of allegations of racism both among players and from fans, prompting renewed debate about the extent of the problem.
Former England captain John Terry received a four-match ban and a ?220,000 ($355,000, 270,000 euros) fine in September after being found guilty of racially abusing QPR's Anton Ferdinand in a game with Chelsea the previous year.
The English game's governing body, the Football Association, is also investigating claims that some West Ham United supporters made anti-Semitic taunts during a match against Tottenham Hotspur, which has a large fan base in the Jewish community.
Similar taunts also greeted Spurs fans in their Europa League game at Italian club Lazio last month.
Serbia and England, meanwhile, face UEFA charges over an under-21 European championship qualifying match that ended in a brawl and claims that fans of the Balkan side directed monkey chants at black players.
Platini accepted that football had a hard job in succeeding to eradicate what he called "this evil among certain individuals" that governments and religions had so far not succeeded in eliminating.
But he said that because of the game's popularity around the world, everyone involved in football should assume the responsibility to set an example.
Source: AFP
Source: AFP