pets are just as much a part of the family as humans are. it's perfectly understandable you'd be feeling that way.

when I was a child, I had no idea that my puppydog was going to die. she had gone to the vet, for what I thought was just a series of tests

but I got the call during dinner: sorry, she has to be put to sleep.... even for weeks after she died, I thought I could hear her in her basket, or rattling the stairgate (which we had to stop her from messing the house)

I loved her and I'm sure this is how you feel about your rat. we're here for you