I think your brake cable releases at the caliper by slipping it out of a slot, but as a more general matter, for those who do have a quick-release lever at the caliper, that's for removing the wheel, NOT for adjusting. That lever should be fully closed when you're riding. Tires, even deflated, are normally wider than the rim, so you can't get the wheel out from the brakes when the brakes are at their working position. The quick-release lever - or the slot where you can slip a cable or housing out of position - lets you release the brake enough to remove the wheel without unclamping the cable.
Once you've finished the installation, squeeze and release the brake lever (the one at the handlebar) HARD several times. This will help the cable and housing seat in their final working position. You'll have to readjust the cable after doing this. With any luck you'll be able to use the barrel adjuster to do that, but it's possible you'll need to re-clamp the cable.
Speed comes from what you put behind you. - Judi Ketteler