Petr Jiracek struck with 18 minutes left to secure a 1-0 victory over deflated co-hosts Poland in Wroclaw, putting the Czechs through to the last eight as Group A winners.
"We started improving at the end of the first half but during the break I told the players to be patient and to be careful at the back," Bilek told a news conference.
"We were patient and we were able to counter attack because they opened the defence."
Jiracek collected a pass from Milan Baros and cut inside a defender before slotting past keeper Przemyslaw Tyton for his second goal of the tournament.
The Czechs advance with Greece, who upset Russia 1-0 in Warsaw, and will play the runners-up of Group B in the last eight.
Bilek hailed the performance from a Czech team missing injured captain Tomas Rosicky, who was not able to run on a sore Achilles in a pre-match fitness test.
Daniel Kolar led the Czech attack in Rosicky's place but much of the damage at Wroclaw's Municipal stadium was done by Vaclav Pilar, whose trickery and pace on the wing gave the Polish defence headaches all night.
"Rosicky tried it before the match and he couldn't start so it is difficult to say if we will have him for the next match," Bilek said. "We are aware he is irreplaceable but Kolar played a great match."
