I was about 11 years old when my hamster died. I was heartbroken. And I felt so very guilty. I had left the cage in the sun, and he probably died of heat stroke. Oh, wait, he was 3 years old! A very old age for hamsters.
I was 27 years old when my dog died. She was a present from my brother when I was 13. We had just moved into a house (previously an apartment, hence the hamester type pets!) and he got me a dog for Christmas. Without telling my parents!!! Anyhow, when my dog died, I went to bed that night and I just thanked God for giving me that dog. My grief was really overshadowed (over sunned) by my gratitude.
I learned a lot from the death of my dear puppy. Years later when my mother died, I was sad, my biggest fear all my life was what happens to me when the person who loves me the most dies? And then GRATITUDE!!!! How lucky am I?! I was, and still am, so completely loved by my mother. And I loved and still do love my mother.
Don't focus on the guilt or the sadness. Focus on the gift of love!