That reminds me of when we moved into our new house a few years back. My cat, who I've had since before I even met my wife, disappeared the day we moved in. Some friends had been helping us move so I was just SURE he snuck out during all the door opening. We looked EVERYWHERE, including around the neighborhood. I was absolutely devastated (this cat is the closest I've ever been with a pet). Even cancelled dinner with friends because I was so upset.
Then about 2 hours later my wife finds him. He was hiding underneath an ottoman. Now you might be saying "But I thought you looked everywhere?". Well, I didn't mention that this is a 28 lb Maine **** cat so I never in a million years thought he could even fit underneath an ottoman with about a 4" clearance LOL.
OP, no reason to feel like a bad person or "parent". Just a lesson learned.