Oleg Blokhin's side, who will play all their Group D matches against England, France and Sweden at home, lost 2-0 in the friendly on Tuesday night in Ingolstadt in southern Germany.
Blokhin, a Ukraine football legend even though in his stellar playing career he was obliged to play for the Soviet Union, dismissed fears about his team's poor form going into the tournament, saying 10 of his players were suffering from food poisoning, forcing him to change his line-up.
Ukraine play their first match against Sweden in the capital Kiev on Monday.
France and Sweden are the only foreign teams out of the 16 nations taking part to base themselves in Ukraine. "Les Bleus" are due to arrive in Donetsk from Paris later on Wednesday. Sweden are also expected in Kiev around the same time.
England have chosen the southern Polish city of Krakow for their base and will travel to their three matches in Ukraine by plane. Roy Hodgson's team are due to touch down late afternoon on Wednesday.