When I was little we had a hound dog who hunted rabbits, but would take a baby rabbit home to nurse and raise it. It seemed that they would not usually make it to adulthood, and we would end up burying it in the rabbit cemetery, where lied Hoppy I, II, and III. We sure would cry when we lost one of our wild babies, whether they be bird or mammal.
Bless you and your dog. I cry when I lose my furbabies too.