But Bilic believes Gunners fans will soon see that Arsene Wenger has made yet another shrewd signing.
Bilic said: "He is a brilliant player, definitely one of the best strikers in the world.
"It is early days for him at Arsenal. Wenger always takes time with the new guys. I speak to his assistant Boro Primorac, who is Croatian, every week.
"I'm sure Eduardo is going to be a great player for Arsenal. They are delighted with him."