Bilic's side squandered an opportunity to kick further clear in the Championship's automatic promotion spots after being held to a goalless draw by the Blues following third-placed Fulham's 2-0 loss at home to fourth-placed Brentford.
The stalemate still put the Baggies above Leeds United who are now second on goal difference but Marcelo Bielsa's Whites would move three points clear of West Brom and establish a ten-point cushion in the automatic promotion spots if taking a victory from Sunday's clash at Cardiff City.
Leeds then take on Fulham at Elland Road next Saturday as part of a huge weekend which sees the top four play each other with West Brom travelling to Brentford on Friday night.
Brentford are now only one point behind Fulham who are seven points behind both West Brom and Leeds though United have a game in hand.
Assessing his side's display against Birmingham, Bilic told Sky Sports: "We played good.
"I'm happy with the effort, I'm happy with the controlling of the game, I'm happy with the composure, I'm happy with basically everything apart from the final product.
"I didn't see the stats but my analyst told me 21 shots, two on target only, 35 crosses, some of them were great crosses but it was missing - that kind of quality in the box which is mostly not skill but sharpness. That is understandable that you are lacking that in the first game.
"Of course I am not happy with the result but we couldn't score a goal, that's the whole story.
"We tried enough and we have done everything but we were just lacking that bit of quality.
"We were enough times there, we were enough times in front of their box - shots, crosses, everything, corners, great balls and you are expecting a goal but a few times the ball is crossing the six yard box. We just weren't there."
Asked if his side would be sharper at Brentford on Friday, Bilic said: Yes, the first game is the first game. The players also have those questions of how am I going to look like because training is training and a competitive game is something different.
"Of course it will be better so I told the guys, of course we are not happy, we wanted to win the game, but be positive and build on this basically.
"We never thought it was going to be easy. We are gutted that we didn't win the game but we are good."
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