I don't. I understand the principles of the stuff I use and can draw upon past experience to analogize to new stuff. Like, despite what a lot of the Node community will tell you, a Reactor model on N threads (where their N = 1) is not new. I saw it in Java, with Netty, most of a decade ago and you see it today, albeit abstracted from you a little, in Play. At a gig last year, I was able to build out a plan of attack for scaling out a Ruby web server infrastructure pretty easily (despite not knowing Ruby or Rails) when I learned that EventMachine was yet another similar system. At some point, the principles stick, and the stuff on the surface just chances. And that--whatever. You can pick that stuff up and set it aside whenever.
Wordpress? Just another CMS.
Joomla? Just another CMS.
JSON? Just another interchange format.
That said, I'm convinced at this point that, barring the very occasional unicorn, measuring yourself against other people who claim to be "full stack developers" is really just a way to make yourself feel bad. "Full stack developers" are stupefyingly rare, despite every startup you see on here trying to say otherwise. It's the new "rockstar" or "ninja". I used to call myself one, but I was a liar. My "stack" skills include "debugging MySQL with gdb and strace" (this has happened, and it was terrible), but doesn't include "JavaScript flavor of the week" because I just have no interest in it. Other folks are more than happy to keep up on the cutting edge of JavaScript, but their conception of a "stack" ends at "well, I tried to configure nginx and it didn't work" (or even higher than that, at "Rails did X but I don't feel comfortable diving in and figuring out why").
Just do what you can, and don't beat yourself up over what you can't.