Yeah, I'm in the same boat - should be defending my dissertation this spring. I arranged a postdoc because I don't feel ready for a tenure-track job. I can completely sympathize with not feeling adequate to apply for jobs or worrying too much about not getting them to even apply.

Don't talk yourself out of trying and taking risks - the things people regret in life are the ones the didn't do and the risks they didn't take. Living a "safe" life doesn't tend to be very fulfilling and may lead to a lot of regrets. That's why I pursued my PhD even though I was not confident I'd be able to do even that.

For me, it's one of those "just do it" things. You might not get the job if you apply, but you definitely won't get the job if you don't apply! Although I was feeling completely inadequate when I was hunting for faculty jobs, and only sent out 3 apps (omg, so much work!) one of them wanted a campus visit - by then I already had the postdoc set up, so I declined, but it made me feel a lot more confident about my ability to get a job and (hopefully) handle it once I've finished my postdoc.

You know your limits better than anyone else, but try not to underestimate yourself either. Good luck!