How embarrassing is it if you don't come out and speak to your parents' friends and your mother lets them know that you're not saying hi?

I went to visit my parents this weekend on a last-minute trip. My parents had already scheduled friends to come visit while I was there. I was tired, looked awful and had work to do, so I told my mother that even though it'd be politer for me to say hi, I'd stay in another part of the house and work, and wouldn't say hello.

The friends came to visit for a few hours for dinner. I worked and was happy.

My mother then told me that she had announced to everyone that I was in the house, working, while they were there, and that she had asked me to join them but that I had refused.

How embarrassed would you be if you were me? (Yes, I know that I should have come out and said hello to everyone, but I thought that they wouldn't know that I was there.)

Thanks.