Both sentences are natural. There are differences in meaning. "to be left home" doesn't mean that you must be physically inside your house. It just means that you have not left the general place that you live. "My family went to visit relatives in another city, and I was left home alone." Although I was left home alone, I can still leave my house to go to work, to the store, to the park, etc. The second sentence does mean that you are physically inside your house. "My wife and kids went to sit outside for 15 minutes, and I was left alone in my house."

You can say: I was left at home all by myself.

Thank you very much for your explanation, Neil! I understand very well! Thank you for the alternative expression, Jura!