I'm so sorry for your loss. I totally understand your frustration, anger, and sadness. Dogs are dogs, and the prey instinct is always there. But that's dogs; we sometimes try to put our human rationale on our pets (I know I do!) and are surprised - often very badly - when our dogs act just like dogs and do something we didn't think they'd do. I certainly learned that when my elderly dachshund, which had never seen a chicken in his life, killed 3 of mine over a period of a month. After the first one, I began to be more vigilant, but still missed it when there was a spot in the run fence one of the chickens exploited and got out.... dashing right past Zorro. She ran, he chased, and got her before I could get to either of them. Now Zorro is my very best predator-proofing fellow: I watch where HE tried to get into the run, and secured all those weak spots.
Now that the chickens are older and much larger, I can walk with him whilst they free range in the back yard - BUT I MUST KEEP AN EYE ON HIM ALL THE TIME. Luckily, the rooster fluffed up, stood up tall, flapped his wings to become enourmous and lunged at Zorro, screaming bloody murder. Zorro isn't about to chase HIM, ever.
I love my little dog - had him nearly 12 years. It's not his fault he killed those chickens, it was mine. But I sure was mad at the situation. And myself.