Guilt (animal death)

I was walking to get coffee, I saw a cat I like saying hello to cats. I walked up to it and it bolted into the road and was hit by a car that has just roared away from the curb, the cat was crushed and took a long horrible time to die, it died because I selfishly wanted to engage with it. I am riddled with guilt a physical all consuming feeling, for the cat and my wife who also had to see the accident.

I don’t see a way past this.