My loss experiences were in reverse, I lost my mother before my pets. But the loss of my pets hit me much harder because they had been a positive part on my life.

I imagine that quite a few people struggle after the loss of a pet specifically because they think - and maybe are also being told - that they shouldn't feel as bad as they do because "it was only an animal". The first step in avoiding lasting psychological damage is accepting that the pet was just as important to one's life as people are, and that that is okay.