Croatia required a play-off to reach their fourth finals in five attempts.
They started their qualifying campaign with three wins from four games before losing 1-0 away at Georgia.
That allowed Greece to take advantage and although Croatia embarked on a three-game winning streak, a 2-0 loss in Athens saw them slip up again.
Bilic was strongly criticised but clung onto his job and orchestrated a victory over Turkey in the play-off.
The Croats won 3-0 away in the first leg in November before holding Turkey to a 0-0 draw at home to reach the finals.
Croatia were then beaten 3-1 at home by Sweden in a friendly in February before winning 3-1 against Estonia on May 25 in a pre-tournament warm-up.