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."
Economic troubles, a severe winter and political tension have led to long delays in preparations by the ex-Soviet republic of Ukraine ahead of the 16-nation tournament.
It is five months behind schedule with particular problems in Kiev, which is due to stage the final, and Lviv.
Ukraine has already announced weekly auctions of treasury bills to help raise cash for Euro 2012 - effectively adding to rising domestic debt problems. It also plans to launch a national lottery later this year.
GOVERNMENT PLANS
Euro 2012 minister Borys Kolesnikov, earlier on Wednesday announced government plans to stump up 26 billion hryvnias ($3.3 billion) from the 2010 state budget to help modernise stadiums, develop airport infrastructure and build roads.
The government also announced a national agency had been set up to oversee preparations.
Ukraine plans to host matches in Donetsk and Kharkiv as well as Kiev and Lviv.
Earlier this month, Ukraine's new president, Viktor Yanukovich, added to the despondency by saying preparations for the tournament were "in terrible shape".
Yanukovich said 40 billion hryvnia was needed to catch up, but he stressed Ukraine would do everything it could to finish work on time and avoid a national disgrace.
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.
Later on Wednesday, in the industrial eastern city of Donetsk, Platini said each of the four Ukrainian cities had its own specific problems and priorities.
"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.
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