Bilic's team were top seeds for the qualification draw but finished third in their group behind England and Ukraine. However, the former West Ham United defender - who has been linked with a return to the Premier League - insisted neither he nor his coaching team were going anywhere.
"We won't resign as the Croatian FA, players and people involved in football want us to stay," said Bilic. "We are fully motivated and eager to carry on our work.
"I talked with FA chairman Vlatko Markovic and secretary general Zorislav Srebric. They both said they wanted us to stay on. We'll keep most of the team, only small changes are required for the EURO 2012 campaign."
Bilic was appointed Croatia manager in July 2006 and he is expected to be awarded a contract extension when the Croatian FA board meet next Friday.