At the start of a tour of Ukraine's four host cities, Platini said the stadiums in the capital Kiev and the Western city of Lviv were far from nearing completion but UEFA was pinning its hopes on the assurances of the authorities.
"We have trusted in Ukraine for a long time already and we have trusted in Poland for a long time, and we would like to see that things are moving in the right direction," he said in translated remarks.
But he warned there could be no "step backwards", adding: "(The) Euro takes place in 2012 and it will never take place in 2013. That is why now some decisions have to be taken."
Earlier this month, Ukraine's new president, Viktor Yanukovich, added to the despondency by saying preparations for the tournament were "in terrible shape".
Platini reminded his Ukrainian hosts, however, that European football's governing body had made it clear the Kiev stadium in particular had to meet certain standards to avoid Euro 2012 being taken away from the country.
"The executive committee (of UEFA) has already said that if there is no Kiev there will be no Ukraine," he said.
"In Lviv, the stadium is not completed but there are lots of hotels. In Donetsk, there is a fine stadium but for a city that will hold a semi-final there are few hotels," he said.
