Assassin's Shroud isn't an attack power however. Technically it isn't an attack despite the fact that it "requires" an attack roll. If the attack misses the shroud's effect goes off regardless, probably damaging and thus killing the minion..
No, the assassin shroud power very clearly states " Before you make an attack roll against blah blah invoke all or none of your shrouds..blah....The attack deals 1d6 damage per shroud, minus 1 shroud if the attack misses...". (dragon 279 page 8, text of the assassin's shroud power)
Its the attack dealing the shroud damage, thus minions still take no damage on a miss. Its pretty straight forward. Shrouding minions should be a waste of time, and fortunately, it is.