Some would think it silly... ridiculous even... to express grief over the loss of a pet. You probably won't be too surprised to know I don't rank amongst them.
Believe me when I say I feel I feel the loss of a pet, or indeed, the death of all sorts of creatures, more than is probably good for me. A rescued rabbit (literally rescued from under a hedge having been discarded in a car-park) caused us both disproportionate sadness a couple of months ago when she died in my arms.... so I am very much aware of the unhappiness the loss of your moggie will be causing at the moment. I shed buckets and buckets when our cat died a good few years ago (another rescue .. this one turned up at my Fire Station and attached himself to me). But, of course, the sadness eases, as it does when we lose parents and relatives etc. The ability to feel fondness and to care for creatures says something about you .. and all those others who genuinely love and cherish their animals and, in my opinion, it makes you a better man.