This is my situation - I only really found out I loved code in University, and only worked out what I really need to do to do that kind of work I want to do since entering employment. I'm still relatively young (24) but even I feel this experience gap in talking to potential employers.

That said I'm now actively building a portfolio by working nights on real products and leveraging what experience I do have as heavily as I can. I also try to present how quickly I picked up the skills I do have in things like Ruby, coffee/node and all that 'sexy' stuff to show that I can pick up anything anyone throws at me really quickly.

Hopefully by the end of the year I'll be where I want to be.