Anakin didn't think he killed her. Just before he tore apart the operating room, he tells Palpatine he "felt" she was alive when he last saw her. Palpatine tells Vader he killed her.
Well, he believes it after the Emporer tells him that he killed her in his anger. This explains his obsession with finding Luke at the beginning of ESB. He is so attached to family (his Mother and then his wife), that the idea that he has a son becomes an obsessive fixation for him.