That's a tough question, Max. The animal you see nosing around the carcass or even eating, may or may not be the one that took your pony down or ran him to death. I've lost critters too. And sometimes I've blamed the wrong one. Sometimes the evidence seemed really obvious, and I still got it wrong. Just be sure. I've seen the wrong domestic dog get shot for something he didn't do. Getting a second opinion helps.
Sometimes I, myself, have been wrongly accused. I've seen it happen to others, and I've made a couple of wrong assumptions about my fellow man as well. A false accusation can be one of the hardest things to live with.
Shooting critters that I know are bothering my livestock? Yes. But ........ we can never call that bullet back. Make your choices wisely.