Very sorry to hear of your lost Gov. I've gone through the same thing as you when I was a teenager.... mom's dog and two cats had to be put down and to make a long story short, I stuck by their sides while they were being injected and promise myself that I would never do it again.... It's a tough decision to make and tougher to be there by their sides when it's unfolding.... I still have vivid memories of the events.
I think you did the right thing, your friend is in a better place right now and it's not suffering anymore.
Time will heal
Leechman