No no, the crown should be in an unlocked room in the marsh cave, in a treasure chest guarded by a group of Wizards (well that's what they are called in the NES version and in Origins). You need the crown to get the crystal ball, which you need to get the herb, which you need to get the mystic key.. so requiring the mystic key for the crown wouldn't make sense. I know there are rooms in the marsh cave that can only be opened with the mystic key, but they only have regular treasure in them. Well that's how it is in the NES version and Origins
You probably just missed the room with the crown.