I think the term is 'shoot, shovel, shut up'

The 3 S's.
There is always going to be a big chasm between hunters/protectors and non-hunters. Not all shots are clean kills no matter how badly that you want them to be. It bites but it happens and you always cannot follow the animal you have wounded to give it a killing shot. I shot a ground hog once that was threatening one of our dogs. Went back to reload, came back, ground hog was gone and I couldn't find it.Hated it but it happens.
When you live on a farm you get a different POV about things. I have spent a lot of money on my birds, just as our Amish neighbors have spent a lot on their goats, cattle, sheep and horses. Yet each year the Amish men get together in January and go on a predator drive and shoot. Then try to take out all the small and large predators that they can before lambing/calving/kidding season. From what I've heard, not every first shot is a lethal shot and one of the predators they shot was a mountain lion. It took three shots to dispatch it.
Each infant taken by predators (I've heard nightmare stories of a coyote dragging a lamb across a pasture, tearing at it all the while, torturing it before it is killed and it's mother helplessly following) is money out of their pockets and food out of their large family's mouths. Each chicken taken means no eggs and no fried chicken for Sunday dinner.
We understand that predators need to go. Period. There are hundreds of miles of forrest timber around us that they are welcome to hunt on all they want, including our own timber. But bother my chickens, all you four footed foxes, raccoons, possums, coyotes and yes, mountain lions and you will die. True I will try my best to give you a quick and clean death but if I don't, at least I know that you will not be back to kill my livestock.
My unspoken contract with wildlife is that unless you are a deer, or threaten my husband, myself or one of our dogs, I will not hunt you in your home or threaten you. But bother my family, my pets or my chickens and all bets are off.
I'm glad you got a shot at the fox. Even if wounded and recovers, it knows that you are now a threat and will probably avoid your territory. Only a fox knows how a fox thinks so keep your eyes open and stay alert.
Sorry if I've stepped on toes but this is my humble opinion and I am entitled to it.