The 47-year-old lamented his side's heavy defeat to the Russians in Wroclaw, but insisted that his country will improve as the tournament continues to unfold
Despite a bright opening, the Czechs were outplayed by Dick Advocaat's men, with Alan Dzagoev and Roman Shirokov both netting to give the Russians a commanding half-time lead.
Vaclav Pilar reduced the deficit with a fine finish, before Dzagoev netted his second of the night, and Roman Pavlyuchenko wrapped up the win to send Russia on top of Group A.
Bilek, who signed a new deal with the Czech Football Association (FACR) shortly prior to the start of the tournament, voiced his frustrations at his side's display but did not discount the strength of their opponents.
"We had a fairly good start to the match, the first 15 minutes we kept the ball well, we played well. Then we started to have problems when we lost possession in their half, they counterattacked us very quickly." the coach told isport.cz.
"Logically, we are all disappointed, the result is underwhelming. [Conceding] four goals is very annoying. [We] must show strength and character. We will analyse our mistakes and go to the next match."
"Everyone is disappointed right now. We imagined that the result would be different. We often lost the ball, [and] an improvement is necessary." the former international later told CT4.
The second round of Group A fixtures takes place on Tuesday, with Russia taking on co-hosts Poland in Warsaw and Czech Republic encountering Greece in Wroclaw.