The 47-year-old boss conceded his tired team were second best as Cristiano Ronaldo's crashing header was enough to seal the Seleccao's passage to the semi-final
|PORTUGAL 1-0 CZECH REPUBLIC
The Real Madrid frontman was twice thwarted by the post and also found Czech shot-stopper Petr Cech in inspired form, but he pounced 11 minutes from time to send Paulo Bento's side through.
And the 47-year-old coach admitted his side had struggled to pose a serious threat to the Seleccao.
"The Portuguese were the best side, much stronger in a footballing sense," Bilek said after the game.
"Their attack is very strong. Petr Cech pulled off some stunning saves to keep us in the game.
"We had wanted to play with a solid defence and rely on the counterattack, but we started to run out of energy during the second half.
"And one situation was enough to decide [the match]."