"People here feel there are too many problems to host this tournament. Can we host it? I really don't know."
Italy was widely expected to win the Uefa vote for Euro 2012.
However, their bid was overshadowed by a referee corruption scandal and problems with football-related crowd trouble.
Scotland's First Minister Alex Salmond is a keen football fan and has voiced his interest in the nation hosting a major event.
"I've had discussions with Alex Salmond and the Scottish government and they would like us to apply for a tournament," added Smith.
"We know about the criteria that has to be met and there is a financial cost to that, so we'd have to see if that money could be raised by government."
Hampden Park, Ibrox, Celtic Park and Murrayfield, the home of Scottish rugby, all meet international standards.
But another four stadiums would have to be constructed or upgraded in order for Scotland to succeed with any bid.
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