I was only about four years old when my first dog died so I didn't completely grasp the concept at that time.
Our second dog (and first Welshie!) was just shy of 15 when she died...we got Winnie when I was 4 or so and she died a few months after I turned 19. I was completely devastated by that. I was very attached to her. She was very much a member of the family and I cried quite a bit. I still think about her a lot.
I am sorry for your loss.
It is very tough to lose a pet.