Platini, addressing delegates from 53 member nations at UEFA's congress in London on Friday, said money-laundering and corruption, as well as hooliganism and doping, were "scourges" on football.
"We are protecting our sport from this scourge with all the means at our disposal, but, unfortunately, that is sometimes not enough," Platini, who claimed his appeals for a specialist force had been ignored for six years, said.
"We are not dealing with petty criminals who are looking to make ends meet. It would seem that we are, in some instances, dealing with mafia-type organisations that are using certain matches to launder money, tarnishing our sport in the process.
"We can take reassurance from the fact that this is far from being a widespread phenomenon. However, just one fixed match is one match too many.
"Six years ago now, in response to this problem of betting, corruption and match-fixing, as well as the problems of hooliganism and doping, I called for the establishment of a European sports police force.
"There has been no response to those calls so far. Given the absence of any reaction and the lack of awareness on the part of politicians, I renew that call today.
"And if, by misfortune, this call again falls on deaf ears, I ask that each country, at the very least, adopts specific provisions of national legislation
addressing the issue of match-fixing, in order to finally have the legal tools necessary to rigorously punish these cheats."
Only 10 of UEFA's 53 countries- including Britain - has legislation to outlaw match-fixing, said Platini, adding: "That's not many, and not enough."
Speaking at the event, ahead of Saturday's Champions League final between Bayern Munich and Borussia Dortmund at Wembley, Platini also praised the Premier League and Football League for bringing in spending controls akin to UEFA's financial fair play rules.
"In order to prevent the current system from collapsing and stop the bubble from bursting, UEFA had a duty to step in, and it will be up to independent bodies to punish the few clubs that have not realised that football can no longer live above the rules," Platini said.
"The Premier League and the Football League have themselves grasped the
importance of this matter and the need to adopt financial fair play. In this respect, I congratulate England's professional clubs."