Czech coach Hasek angered by late Portugal winner
The Czechs had soaked up Portugal's first-half pressure under torrential rain in Leipzig before stunning one of the pre-tournament favourites early in the second period.
Lukas Provod's spectacular strike from outside the box left Diogo Costa helpless.
However, the lead lasted just seven minutes before Robin Hranac's own goal levelled and Francisco Conceicao smashed home his first Portugal goal in stoppage time to give Roberto Martinez's men all three points.
"I was angry. We played against one the best teams in the world and it was a draw (until stoppage time). It was a real pity to concede in the last minute but you saw their qualities," said Hasek.
"We didn't make it easy for Portugal, when we were defending we didn't give them that much space to create.
"Our defence worked really well even if we were really deep. We didn't want to be but Portugal have great quality in attack and forced us back."
Next up the Czechs take on Georgia on Saturday.