It really isn't silly, OP, I'm so sorry about your beloved cat. 
I remember how devastated I was when I had to have my 13 and a half year old companion cat, whose health had broken down through the stress at coping with our new DD, who had come to us aged 1. She couldn't cope with the change and had been over grooming as a result. Then she developed all sorts of other health problems as well, and it just wasn't fair to put her through years of medication when she was so unhappy. The vet also told me that she wouldn't cope with being rehomed either.
It became clear that I had to make the heartbreaking decision to have her PTS. She came to me as a rescue cat at 3 years old, when I first bought my one bedroom flat in London and went with me when I moved away to be with my DH, and through years with infertility.
My DD1 (now 11) was 2 and a half when my cat died and she adored her, the cat's name was her first clear word. She was very attached to her, it was unfortunate that the cat never got used to her, but she was already 12 so it wasn't surprising.
It took me a long time to come to terms with the loss as she was such an affectionate cat. (She won my DH over, too, who had never wanted pets before he met me.) I have 3 lovely furry friends now, and I wouldn't want to be without them.
Please be kind to yourself, OP. It will take time to come to terms with your loss.