That hurts. Every. Single. Time. It never gets easier and I'm pretty certain it get's harder.
I remember my previous dog's last pheasant. He was feeling his 15 years and had a hard time bulling through the brush, but dammit, he was on a hot scent and he was going to find that bird no matter what. He flushed the rooster into the brilliant morning sunlight and it looked like the cover of a Field and Stream magazine. It was so beautiful I almost didn't shoot. But I did shoot because he never would have forgiven me it I had not shot that pheasant after all of his effort to hunt it. That was our last bird together.
I'm sure you have similar memories of Addi. That dog will live as long as you live.