I urge caution in reading this, I was explicit in directions...
Not to be too gory, but why not just disable the attack? Unless you are up against 600lbs of crushing power (you pitbull lovers know what I mean), after the initial chomp the dog will begin to jerk back and forth. This makes things VERY vibrational for you. To defeat the dog(s) all you have to do is take out 2 legs OR break the snout of the dog. Sounds easy, but it isn't. Much more fun than the alternative, though. I don't wanna be dinner for some pups.
This can be done on most average size non-fighting breeds by gripping the upper and lower jaw and ripping in opposite directions. In the event that you are with a fighting breed, do just as they do. Attack the throat. Dig your fingers into the neck, just below the bottom jawline. Find the windpipe and crush. Don't think your strong enough? Wait till the adrenaline of the attack and the endorphins from the bite-hole in your arm hit, then rip him to shreds.
Last resort, for those of us who can, is wrap your arms around his neck from any direction (beneath him, as if he attacked, or above him, as if he is lunging past you). Squeeze hard until he stops moving and his breathing is unable to be heard, then stand up, take a breath. When you have your balance, and before he gets up again, stomp just behind the front legs. This is called the chest cavity, and contains most of the vital organs for the pup. Don't think your heavy enough to crush the chest cavity? Work your way down to where his ribs stop, just before his pelvis and hind legs and stomp the top of him. This is the backbone, and if done properly can and will paralyze his back legs. Ensure that you find a sharp object afterwards and kill him by inserting it into the chest cavity and twisting until he coughs blood (lung puncture, just behind front shoulderblades). This, for a dog, would be mercy because a paralyzed dog will be victim to many and painful bites before he is killed by other dogs.
Brutal? Maybe... More brutal that dying at the hands of a pack of pups? Not likely. Note to readers... Dogs have an instinctual knowledge of where the throat is. Ensure that you keep your chin low and your arms close to your body, or you will not survive the bloodloss afterwards. Your major bloodvessels are vulnerable on the insides of your thighs, the insides of your upper arms, and the sides of your neck. Protect yourself accordingly, it only takes 5 minutes to die from arterial bloodloss in these areas.