The Austrian joined the club for £25m during the summer but has struglled to make an impression.
Arnautovic was substituted at half-time in Saturday's 1-1 draw with Burnley and has also missed four of the club's previous matches due to suspension and illness.
Speaking after the draw with Burnley, Bilic admitted that West Ham's fans are still yet to see the best of winger, whilst also insisting that the decision to substitute him was purely tactical.
"Yes, he has made a slow start," said Bilic.
"But that is because he got suspended for three games and then he missed the last game, because of the flu he got.
"His slow start is because of his mistake.
"This [substitution] was just tactical. He didn't go out because of a bad performance, he was taken off because my staff and I decided we needed an extra man in midfield.
"I think it was a good decision."
Bilic is likely to face a selection headache ahead of the visit of Brighton on Friday, with Pedro Obiang impressing against Burnley, Manuel Lanzini having returned to full fitness and both Diafra Sakho and Andre Ayew being forced to make do with a place on the bench against the 'Clarets', not that he sees that as a bad thing.
"It is difficult but it happens to most clubs in the moment they have all their players," said the Croatian.
"Not every team is in the position of Crystal Palace, all the strikers injured or out.
"You have a squad with numbers, because very rarely are you in a position to choose from your whole squad."