Grief! Oh my Lord, I still sometimes shed a few tears about our last cat Smokey, who was put to sleep two whole years ago. I think it's natural for sentient beings (humans, dogs, cats etc) to grieve after a loss.
Don't elephants show signs of grief after a death?
My funny neighbour-across-the-road was going to summon the men in white coats when I confessed I'd had a 'pet bluebottle fly'. I fed him tiny pieces of ham in our kitchen, and when he died I was rather sad. (She swats hers with enormous pleasure)