"We are happy to collect three points from the opening match which is always tough. I am not entirely happy with the performance in the second half, but we were very good in the opening period and should have led by a bigger margin at half-time," said the former Croatia player.
Luka Modric put Croatia ahead after only four minutes. Co-hosts Austria took control of the game but failed to level the score and got their opening party ruined.
"The early goal helped us a lot. We controlled the first half flawlessly, but then withdrew to the defense too much. We gave the Austrians too many free-kicks in the second half," added Bilic.
The Croatian knows his men can't do such mistakes against the Germans on Thursday if they want to secure a place in the quarter finals.