The three points, courtesy of two Andriy Shevchenko headers, mean that the co-hosts are well-placed to reach the last eight though they first have to tackle France and England and Blokhin says there is plenty of work still to be done.
"There is no reason for euphoria," he told reporters. "We just won a match and as coach I am never happy. The lads were a little surprised I was not happy after our debriefing session. They were a little euphoric - but there is no reason not to keep our feet on the ground.
"We saw the last ten minutes it could all have gone wrong," said Blokhin, whose men face France on Friday in Donetsk. "I don't think it was the greatest game in Ukraine's history - there were many errors. Some can be ironed out but for others there is not enough time."