If you recognize the cat as a neighbor’s or—your heart cracks here—your own, allow yourself a moment. This isn’t a joke. Cats are family. My friend once found her tabby under the hydrangeas and spent an hour just sitting in the grass, crying and talking to him. That’s allowed. That’s human.
Wrap the cat in a soft blanket or a pillowcase—something that feels gentle. Many vets and shelters will hold the body for a day so you can decide on cremation or burial. Check your local laws; in most places, burying a pet in your yard is fine, just dig deep enough (at least two feet) to keep other animals from disturbing it.