When I started Aikido, I made a deliberate point to give myself permission to be unashamedly ignorant. The idea of feeling embarassed about being unskilled at something I had never done before just didn't make sense to me, so I felt completely free of the kind of self-effacing worries described here. It was great!
As I related elsewhere, I already had a hakama, so I wore it. I occasionally took a rough fall or a punch that someone assumed I should see, but so what? I always felt a little out of my depth, like I didn't quite know what was going on, but I just dealt with it and didn't let it slow me down. I learned a lot, and I learned fast, and in retrospect, it was probably the most fun period of my entire martial arts experience.
Take all that worry and tension and doubt and just let go of it. It's boring and nobody cares about it but you. Be present and alive and do your best - it will leave a much more positive impression on people than whatever slightly improved skills you imagine you should have would.