Turkey rejected the suggestion that it represented a risky option after being pipped 7-6 in the final round of voting.
"We are devastated. This was our third bid so it is not much consolation to know that we lost by a small margin," said Turkey's Euro 2016 bid manager Orhan Gorbon.
"Losing is one thing but it is an underestimation of Turkey to say it was not capable of hosting a larger tournament.
"I don't understand why France should be seen as the safe option."
Platini admitted the contest had put him in a difficult situation - he is French, but of Italian descent and enjoyed his best playing years at Juventus.
"It was not an easy situation for me - I am French, my name is Italian and I have many friends in Turkey. But Uefa has proved once again that we have democracy."
French President Nicolas Sarkozy and former national team star Zinedine Zidane supported their country's case in a presentation to Uefa's ruling executive in Geneva on Friday.
The French government has pledged to help guarantee the projected 1.7bn euro (£1.45bn) cost of building and renovating stadiums despite the worldwide economic problems.
"When I spoke to the French Football Federation, we asked ourselves whether we wanted to be candidates in the middle of a crisis," he told the ceremony during the French presentation.
"But sport is an answer to the crisis. It is because we are in a crisis that we need sport. Nothing is more powerful than sport and, within sport, nothing is more powerful that football."
France's winning bid for 2016 consisted of 12 venues - the Stade de France where France defeated Brazil in the 1998 World Cup final, Paris Saint Germain's Parc des Princes, Lens, Lille, Bordeaux, Nice, Toulouse, Marseille, Lyon, Strasbourg, Saint Etienne and Nancy.
Zidane spoke of being a young fan in the Marseille stadium watching Platini's extra-time goal carry France past Portugal in a classic semi-final in 1984.
Zinedine Zidane was part of France's bid to stage the tournament
"That is the type of experience I want to live again," said Zidane. "Winning is beautiful but it's great to see all the people in the streets partying. This is what I would like to give my children."
Platini added: "It was a very narrow decision - the work done by all three federations was outstanding, and I would like to congratulate the French.
"It has been a complicated situation from the outset and I believe there is a sigh of relief from French football, and they can now upgrade all their stadia to make them up to the same standard as other countries in Europe."
Turkey were bidding to host their first major football tournament while Italy's chances had been written off after a critical review of their bid following Uefa's inspection visits.
Problems and delays in Poland and Ukraine, who will jointly host Euro 2012, may have persuaded Uefa's executive committee to avoid choosing Turkey, an untried country.
"We all did our best," said Turkey President Abdullah Gul, who had called on Uefa to take a "historic decision" and help bring Turkey, which has a Muslim majority, closer to the heart of Europe. "We are saddened that it was lost by one point."
The 2016 event will feature 24 countries for the first time, up from 16 in 2012, as France becomes the first country to stage the European Championship three times.
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