Oh no, I am in tears reading this.
I know how much you adored Jet, you will miss him terribly.
So sorry this has happened to your special boy, but please don't blame yourself.
We have all done the same and luckily most of the time nothing bad happens - you were just so so unlucky. Comfort yourself with the thought that Jet was happy and loved in the short time he was with you - as we all know a lot of dogs never know that.
By the sound of it he knew nothing about it so didn't suffer - harder for you than for him.
Be kind to yourself, you must still be in shock.
Run free Jet.