Perhaps it's not so much a lack of confidence, surely you're scared to do something new? You won't know if you don't try. Lots of jobs offer full training at the lower end of the scale and are glad to take on someone with little or no experience, as this means they are cheaper to employ. I was always quite shy but I applied for a job (that if i'm honest I didn't fully understand what it was), and got it. I'd chucked myself in the deep end of media sales!!
Also, when you do get applying, don't be disheartened by a lack of communication from them, just apply for loads more.
If you're an admin assistant, how long have you been doing it? Is there no potential to move up within the company? What's your dream?