After a year of political instability in both countries, Platini said the next few months would be vital for getting things on track for Europe's showcase tournament.
"I have the distinct feeling that the next four to six months will be crucial in order to avoid any critical slippage in sports and public infrastructure projects and to protect the global credibility of the Euro project itself," Platini said at the close of a two-day UEFA executive committee meeting.
His stern comments came amid recent speculation that UEFA could move the championship out of Poland and Ukraine because of organizational delays.
"UEFA is totally committed to do everything possible, in the next few months to assist and support the two associations ... in order to guarantee the success of the project," Platini said, adding that there are problems with "all infrastructure" in the two countries.
UEFA general secretary David Taylor said it is imperative that action is taken now.
"Political instability and infrastructure deficit are too big at this moment," Taylor said. "It is too late to wait - we need action."
UEFA said it had taken a "momentous decision" last April to award the championship to the two Eastern European countries, ahead of bids from Italy and a joint candidacy from Croatia and Hungary.
"It is clear that there has been a certain degree of political instability in both countries in 2007," UEFA said in a statement. "However, this instability now seems to be over with newly established governments in each country, but there can be no doubt that the launch of investment-intensive projects, such as stadiums, airports and motorways has suffered from the instability."
Platini urged the governments to be "aware of the crucial need to set up a governance and management structure to lead all the projects related to UEFA Euro 2012."
Taylor also said that the prospect of possibly increasing the number of teams at UEFA tournaments to 24 will be discussed at Thursday's UEFA congress in Zagreb.
"We will present a general project of enlarging UEFA tournaments from 16 to 24 teams," he said. "This is not an easy decision. Right now, we don't have an answer because we have to study it well."
Source: FOX Sports