Ukraine have suffered a shock 3-2 defeat to Austria just a week before the start of Euro 2012.
The tournament co-hosts are in Group D with England, France and Sweden.
Marko Arnautovic's last-minute strike condemned Ukraine to their first loss in seven matches.
Oleg Blokhin's side play Turkey in their final warm-up game on Tuesday before their opening group fixture against Sweden on Sunday, June 10.