hummingbird are not cat friendly

I have many hummingbirds in my garden. Yes in Arizona! They love my aloe vera the best. One time Si caught a hummingbird - which is amazing. Si being sixteen years old, never showing any interest in anything but sleeping and eating. He brought it in the house through the pet door. Hearing low growling sounds, I rush to find the problem. It was Si with a bird in his mouth. The bird was dead :( For the longest time after that, I had another hummingbird that kept trying to go through the pet door. I had to put a small curtain rod with a towel around it up above the pet door to kept the hummingbirds away from the door.