There is no "adjustment" for a valve core...it's either screwed all the way in, or not. And it needs to be all the way in..
Just go to any local auto parts store and pick up a small kit that will include a valve core tool and several new cores. Only a few bucks. It's possible that the one your having trouble with is bad, and if so, just replace the core. Its a two minute job, and half that time will be spent letting air out of the tire.
I always keep a few spare cores and a core tool in my tool box.