I grew up in the country, and whenever we lost a pet, we had a burial and a little ceremony kind of thing for us kids to remember them and sort of say goodbye.
After my mom died, we took the grandkids to her graveside and they each wrote her name on a ballon, said something they rememberd about her, then released the balloon...
I'm just guessing that you probably don't have remains, but maybe any kind of ceremony to properly mark the event might help provide some closure.
I don't know. I'm not really good at this kind of thing.
*hugs* though, for sure.