Quoted:
Your night sight contained Tritium which is a radioactive isotope of hydrogen and therefore a gas. Once your vial broke, the gas escaped. There is nothing radioactive or hazardous left in the broken vial. The minute amount of tritium gas that escaped likely posed very little hazard in itself. Besides, tritium is a low energy beta emitter and it is not dangerous externally, as beta particles are unable to penetrate the skin.
I believe it is dissolved in water inside of the vials in most cases, but I may be mistaken. It either case, the beta particles from tritium have barely enough energy to penetrate the skin, so a t-shirt is enough of a barrier to it. However, DO NOT allow any of the material from the vial to get onto your skin as this will allow for tritium o be absirbed into you body. It likely isn't enough to do significant harm, but it will give you an unnecessary dose of radiation. Rinsing the area you got it on with water very well and drinking a whole lot of water over the next few days should be enough to significantly lower any of it's minor effects luckily.
Like others have said, likely not enough to be harmful, especially if you do not get any on your skin; but it is never good to expose yourself to extra doses of radiation, so take some precautions, like wearing rubber gloves when handling it. I am currently a physics student and gave a brief report on this exact circumstance when I was in the Army.