Cutlery does indeed refer to spoons, forks as well as knives.

Yes, I'm afraid that in English, "cutlery" refers to knives, forks, and spoons. In America, we usually say "flatware" instead, although British people use that word with a different meaning. Another term frequently used in America to refer to knives, forks and spoons is "silverware", even if they're made of stainless steel.