Am I overreacting?

So I was sitting on my porch with my parents and there was a cat that walked into our yard. (I live practically in the middle of nowhere by the woods and the only neighbors around us are across a field and behind some trees). I figured it was our neighbors cat because they keep wild cats that they feed sometimes and let them roam around. I went to pet it and it came right up to me and let me pet it. It had big yellow eyes and black fur. It sat by me for a while until my dogs noticed it and started barking. I went inside to go to the backyard to get them to come inside but when I got out there, I witnessed one of my dogs break out of the fence, grab it by it’s neck, and kill the cat. I ran back inside immediately to tell my parents and was sobbing. my mom was saying that I was being a baby and that’s just how the food chain works. I called my friends sobbing because I was so upset and felt at fault for the cats death. I still am really sad sitting here and feeling guilty because I should not have left it alone. I am overreacting like my parents say?