The Frenchman said the stadium in the capital Kiev, which will hold the final, was far from nearing completions, while the stadium in the western city of Lviv "made no progress whatsoever" over winter - a consequence, in part, of adverse weather conditions.
At the end of a two-day visit to four of the country's host cities Platini met Ukraine president Viktor Yanukovych to discuss his concerns.
And with Poland on track to be ready in time, the president of European football's governing body warned there could be no "step backwards".
He added: "The Euros will take place in 2012 and not in 2013. That is why now some decisions have to be taken."
"We have trusted in Ukraine for a long time already and we have trusted in Poland for a long time," said Platini.
"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."
Ukraine's new president, Viktor Yanukovich conceded that preparations for the tournament were "in terrible shape" but he stressed everything would be done to make sure work is finished on time and avoid a national disgrace.
Euro 2012 minister Borys Kolesnikov announced government plans to stump up 26 billion hryvnias (£2.2 billion) from the 2010 state budget to help modernise stadiums, develop airport infrastructure and build roads.
Poland and Ukraine were announced as co-hosts by Uefa in April 2007.
The tournament, the last to be contested by 16 teams before 24 finalists take part from 2016, is scheduled to run between 9 June and 1 July 2012.
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