I screwed up the final. What should I do?
As Nate Eldredge cautions in his comment above, it's probably up to you, not the instructor to submit a withdrawal request to the registrar.  Usually, the instructor's only involvement is to approve or disapprove your request.  But once you've taken the final and depending on your school's policies, it's probably too late to withdraw anyway.

That said, your life is almost certainly not ruined. If you wrote anything at all, you will likely get some partial credit.  And who knows how your instructor will curve the results.  If you had trouble even after doing your best to prepare, it's quite possible others did as well and that the curve will be much easier than either you or the instructor expected.  Sometimes instructors accidentally write a test that's too hard or has errors that make a problem impossible.  (I taught EE at Washington and now teach CS at Michigan, so think about how I would know this happens! :)

Finally, even if your final grade is low enough that you need to repeat, this is still not fatal.  Students are rarely aware of just how many of their peers have to repeat classes.  And guess what, they still get jobs.  Yes, of course I understand why you're upset.  But you're not dead yet.