The former West Ham and Everton defender has made the transition into international management with ease, leading his country to a major tournament during his first qualifying campaign.
Six points from their opening two games, including a 2-1 win over Germany, has seen Croatia book their place in the quarter-finals and establish themselves as dark horses to go all the way.
Manchester City defender Corluka believes much of the credit for their success must go to their boss, but insists that no-one in the camp is getting carried away just yet.
"For us, Bilic is just perfect," he said.
"He gives us belief, but he also makes us relaxed. It was a great result against Germany, but we must not get ahead of ourselves.
"We must focus on the next game (against Poland on Monday). We must take it one game at a time and then we will see."