And that is perfectly fine (as in: natural).
Like I said, a few years ago, my cat passed away too. She was 24, around 2 years older than I am. She came to us when we were around 3 years old, so basically, she lived together with us for as long as I can remember.
Her death hit me really, really hard emotionally; and thinking about it oftentimes still makes me cry today. We didn't lose a pet back then - we lost a precious family member.