Well while your lovely rabbit was alive you gave him/her love and care. That is the greatest gift you can give anyone or any animal. Some animals are predators, thats the way they survive. This instinct you cannot change.
We have a pure bred mini fox terrier. She eats our food, sleeps in our bed and barracks for the bulldogs in AFL footy just like us. She is adored. However we fear that a large dog will jump our fence one day and hurt her. So we are building a tall fence. You can only do your best. Your best is good enough.
People that love animals are very kind and loving people. We give to animals as much care as we can muster, sadly sometimes it just isnt enough against other animals.
Give yourself time and try not to feel guilty. Ask your parents if you can buy a small flowering plant, put it in the garden in memory of your rabbit.
Thankyou for sharing your grief.