The stalemate means that the Turkish club still have a good chance of upsetting the Gunners, who are looking to reach the group stages of the competition for the 17th season in a row, and Bilic believes that their performance will give them a boost ahead of their trip to the Emirates Stadium.
"It was a great game to watch, it wasn't like a usual boring 0-0," the Croatian told Sky Sports News. "It was a very offensive game. I'm so proud of my boys.
"Arsenal had chances, but I think we deserved to win. Our chances were a little bit better. It was a good result for us and we're still alive.
"We go to the Emirates in one week with even more confidence than we had before this game."
The second leg takes place in North London next Wednesday.