Arnautovic put in a strong performance during West Ham's 3-0 victory over the Championship, setting up two goals.
Bilic said: "I could have asked for more. I want him to do more. He's got that quality and that something extra.
"I like him as a player, but sometimes he gets happy with the few things that he does when I want him to push the borders. After what happened last month, this is the beginning of the comeback for him."