Having a dog means it's your responsibility to look after your dog, which among other things means preventing him/her from suffering if you can.
What happened isn't ideal just realise you did what you had to do and didn't have much other choice, accept the kamma of it because the kamma of watching your dog suffer would be worse.
"Whenever we feel that we are definitely right, so much so that we refuse to open up to anything or anybody else, right there we are wrong. It becomes wrong view. When suffering arises, where does it arise from? The cause is wrong view, the fruit of that being suffering. If it was right view it wouldn't cause suffering." - Ajahn Chah
"Remember you dont meditate to get anything, but to get rid of things. We do it, not with desire, but with letting go. If you want anything, you wont find it." - Ajahn Chah