"It is impossible for Ukraine to lose the championship," the head of European football's governing body said at the end of a two-day visit to check on the country's preparations for the tournament.
However, he admitted that there was a lot of work still to be done.
"I think we will be successful, although it will not be easy. To be honest, the situation is complicated, but there is the desire to realize this project," Platini said, warning that "if there is no stadium in Kiev, the championship will not be in Ukraine. If there is no stadium in Warsaw, there will be no championship in Poland."
Poland and Ukraine are co-hosting the tournament, and there have been concerns - now largely allayed - that preparations were not progressing fast enough, particularly over the redevelopment of the main stadium in Kiev.
The UEFA delegation visited to gather data for a progress report to be presented to the organization's executive committee at a meeting in Romania in May, when the cities that will host games will be confirmed.
"UEFA has complete information on the readiness of Ukraine to hold Euro 2012," said the president of the Ukrainian Football Federation, Hryhory Surkis.
Platini said the decisions on host cities would be largely based on infrastructure.
"All the fans should encounter the best conditions," he said. "The executive committee will make a decision in favor of fans and football."
Games will be played in Kiev and three other Ukrainian cities, with Donetsk, Dnepropetrovsk, Lvov, Kharkov, and Odessa in the running.
The delegation now moves on to Poland to check on its preparations for the tournament.
