No, you're not missing anything. Mac OS X's Preview is designed as an all-purpose viewer. While it does have some simple editing functions—scaling, cropping, some image adjustment, "annotations", etc—one would not call it an image editor.
GIMP, if you don't want to spend anything. Pixelmator, if you want something a little more "Mac-like" in its presentation.
I don't know the nature of these image sections. If they're "unsavable" Web photos, there are options other than screenshots. I won't talk about techniques here because the moderators might frown on it, beam me into open space like those poor redshirts in "Children."