The Czechs were up 2-0 after only six minutes, leaving Greece too much to do to get back in the match.
"It was a game that started really badly for us," coach Fernando Santos, whose team suffered only their second defeat in 23 matches since the 2010 World Cup, told reporters.
"We knew they would pressure us and we failed to respond. Unfortunately the first 10 minutes really cost us. We did everything we could to score the equaliser but we couldn't."
"This is a line-up that delivered a very good second half against the Polish team [in a 1-1 draw]. That is why I chose this line-up," said Santos.
"In the last 15 minutes we used our hearts more than our minds and this clearly didn't pay off," said Santos.
"We paid dearly for our very bad start," said midfielder Giorgos Samaras. "We must now go into that last game and grab any chances we have left in the tournament. We wanted the win today. We still have faith in our team and ourselves."
"This third game is a final for us," he said. "The group is still open and everyone can advance so we won't give up. We will keep at it."
