For me it is their vulnerability---so dependent on we human to do right by them---to love, feed, stroke and be there for them. they can never say wha tis wrong or tell us how they feel other than a wag, lick or following our every demand. Yes, they love unconditionally, but if we are smart, we love them back the same way, in spite of their imperfect ways. They give undconditionally but more importantly teach us how to give back in the same way....a powerful two way love.
I am so sorry for your loss. There are no words...cry, mourn, weep....then celebrate their life with photos and memorials. It is very ok to hurt right now. Don't try to stop it---let it go. I have been thru it several times---some expected---some not, and each time it rips my heart out. The losses mount one upon the other and seem to hurt even more with each new passing........but after time a healing begins and I know it is time to share my life with another. With pets we are allowed to be what we can not be with people, ourselves.
A great book on grieving that helped me the first time I really lost a baby pet is Angel Paws, Reflections on the Loss of a Beloved Pet. It really helped me know it is ok to grieve the passing of a treasured companion. It reflects that this pain has a very long history, going back centuries, not a new phenomenon to the modern man. Somehow there was comfort in that for me-----if other lived thru it then surely I can too. Read the poems, the stories, written even from the pet's point of view. You will find comfort.
My heart to you. Love in pet speak.