The 21-year-old did his best to dictate play in midfield but gave the ball away a little too often and was fortunate not to be booked in the first half before the Czechs grabbed a late winner.
Corluka, meanwhile, put in a solid performance at right-back for Croatia as they kicked off with a 1-0 win over the other co-hosts Austria on Sunday.
City's other representative at the Euros is goalkeeper Andreas Isaksson, who is set to appear in Sweden's opening game against Greece on Tuesday looking to put himself in the shop window after a frustrating season at City.
Chinese defender Jihai Sun and Brazilian playmaker Elano have also been in international action over the weekend.
China faced Qatar in a World Cup qualifier and Sun managed to earn himself a red card despite being on the bench after protesting against a decision as China slipped to a 1-0 defeat.
Elano played the first hour of Brazil's surprise 2-0 friendly defeat by Venezuela in Boston, so he is expected to be overlooked for the upcoming qualifiers against Paraguay (June 15) and Argentina (June 18).