It's probably nothing to worry about.
The deeper you go, the more damage is done to your vascular network (blood vessels), so it'll be more difficult to get clotted. The best thing to do is pack the wound with sterile gauze (with a touch of your favorite medicinal ointment -- mine is Polysporin, that stuff is gold), and put as much pressure on it as your comfort level allows. Then elevate your hand and stay as still as you can (watch TV or whatever). Any sudden movements you make will cause localized blood pressure changes and will interfere with clotting, so try to make slow, smooth movements if you have to move.