broken mirrors are superstition dating back to Rome, believing that breaking the mirror would effect ones soul [if my memory is correct] which is why people felt it would bring bad luck. grind the shattered glass into dust or a powder [could be all or a little bit] then bury it is the method for broken mirrors. you could also go with the salt thrown over your left shoulder, that one seems to reverse pretty much everything. [except for a black cat, for that one you turn around counter clockwise 3 times i think] do keep in mind this is superstition, so like with curses, the more you think about it and believe bad things will happen, you will feel negative effects.
another option could be to make a protection jar out of the shards. just a thought.