I agree with Punkrotten in the sense that not-caring is the ultimate goal, but getting to that point is tough.
One thing that really helped me was to realize that the more confident I acted in public, the less out-of-place I looked. In the past I had a tendency to slouch and to speak as if I was unsure of the things I was saying, and my lack of self-esteem was very apparent. It came to a crunch when I saw myself on someone's video camera this one time - I was horribly surprised at how meek and unconfident I looked.
So from the next day onwards, I made an effort to stand upright, to walk and talk slowly and with purpose, and to breathe deeply and calmly when I felt nervous. It made a huge difference. Of course, internally I still feel the same fears we all do, but on the surface I can at least come off more or less the way I want to. It doesn't always work - in my previous post I mentioned nervousness around groups of people in social settings and so I'm still not all the way there, but there is something to be said for fake-it-til-you-make-it.
So I would say practice appearing self-assured externally and see if it makes a difference regarding being less conscious of your surroundings.