I think you may be looking through the wrong end of the binoculars. The main purpose of the U.S. Constitution is to set out a framework of laws that the U.S. government is supposed to abide by.
To our citizens yes. Would we fall under, say, the French Constitution if they get mad at us for some reason? Do you think they would first ask themselves if what they were doing was right to protect their country? I don’t think our troops read the Miranda warning to those they were fighting.