In the past year and a half, my father has been let go from his job, my puppy passed away, and my two 17 and 18-year-old cats passed away. I've been told that it doesn't matter at all and that their lives were worthless; "get over it". I say bullroar.
Just because someone is not necessarily human doesn't mean that their life means more or less or that their death doesn't hurt you.
I'm now close to a year since my cat Gussy died and 2 1/2 months since Sammy died. Do I miss them? Like heck. I don't miss them any less than I did their death days. It's just that the grief comes in less frequent intervals.
I find most comfort in writing a letter to them and sending it off into the wind. I like to think that they know how much I still love them, even though I cannot possibly know who does or doesn't have an afterlife. My therapist also helps a lot in everything that has happened; if you find a good enough grief counselor, you can trudge through just about anything.
Hope this helps anyone who needs it <3