10 years ago I had to have my German Shepherd put down; she was suffering from cancer, and I couldn't take it any longer.
A few weeks later I was watching I Am Legend in the theater, and when (spoiler alert) I could see what looked like the inevitable demise of Will Smith's dog, I hoofed it out as quickly as I could. I was completely unprepared to deal with that, and to this day I've never finished the movie.
I'm sorry you had to have your dog put down. It's an awful decision. When my parents decided to do that for the dog I grew up with, I really hated them for awhile. I didn't have a dog for a long time after that, but now I have a one year old Shiba, and I dread the day when I'll have to make that decision. Hopefully that won't be for a long time from now.
I've often thought that having pets (who will obviously have a shorter lifetime than humans) will help them learn to deal with death. That way, when it inevitably happens to an adult in their life, they will have experience processing it.
That may seem a morbid thing to think about, but everything happens for a reason ... circle of life and all that.