UEFA also responded to demands from its top clubs by awarding a Champions League place to the the Europa League winners, while delegates at the annual Congress of European soccer's governing body unanimously approved a resolution introducing tough new measures to fight racism.
Platini also defended Europe's 15 World Cup places after a hint from FIFA president Sepp Blatter that it should concede some to confederations with fewer.
Platini, in typically bullish mood ahead of next week's FIFA Congress in Mauritius, repeated his call for the formation of a European sports police force, telling delegates in his keynote speech he was upset his appeal for one had been ignored.
"Six years ago now, in response to problems 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," Platini said.
"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."
Platini, addressing delegates from UEFA's 53 member nations, said the issues of match-fixing and betting, discrimination and the financial troubles of many clubs were "poisoning football from within" and a sports police force would help the game deal with its problems.
"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," he added, saying that only about 10 countries had already adopted measures.
Platini was happier about welcoming Gibraltar as the 54th member of UEFA after the tiny British colony was finally admitted as a full member after a 14-year fight to join.
He beamed with delight as Congress delegates overwhelmingly approved its membership while even Angel Maria Villa Llona, the highly influential UEFA vice-president from Spain, applauded the colony's arrival.
Spain long opposed Gibraltar's entry but all legal restrictions were removed when the Court of Arbitration for Sport (CAS) ruled in 2011 that there was no reason why it should not become a member.
Although Gibraltar only has 650 registered players and six teams in its national leagues, it will take part in the qualifiers for Euro 2016.
However, UEFA said Gibraltar would be kept apart from Spain in any competition in which they both participated.
"This is a momentous moment for us," Gareth Latin, president of the Gibraltar FA, told the UEFA Congress. "It means we can now begin the next chapter of Gibraltar football."
Latin later told reporters Gibraltar would only recruit players locally, rather than looking abroad for those with connections to the colony.
"We have our own specific guidelines on who can play," he said. "You have to be a Gibraltar national, you have to be born and bred there and have lived there for a certain number years.
"We have been trying to achieve this for 14 years, and we want to give this to the Gibraltar community and we want to develop our kids so they have a chance to become professionals.
UEFA also took a popular decision in attempting to boost the profile of the Europa League, long regarded as the poor relation of the elite and glitzy Champions League.
Platini said that after months of debate UEFA had decided to grant the Europa League winners entry into the Champions League which would boost the profile of the second-tier competition.
"I have thought about this for a long time, and I am delighted we are upgrading the Europa League," Platini said.
"It is an excellent competition in its own right but needed a boost and it now has one. This year's final between Chelsea and Benfica could easily have been the Champions League final itself and I hope it will now grow in appeal."
UEFA's delegates also adopted a new resolution involving tougher measures against players, officials and fans in a bid to stamp out racism in the European game.
Players and officials will now face a minimum 10-match ban for racist abuse in UEFA competitions while European soccer's governing body will partially or fully close stadiums and fine clubs in its matches.
David Gill, outgoing chief executive of Manchester United, and Wolfgang Niersbach, the German FA president, were elected unopposed to UEFA's executive committee for four-year terms.
- Sports & Recreation