I camped somewhere once a few years ago and the spot was right beside a river. For some reason that river had clay deposits all over the place in it, me and some good colleagues would make cheap potery out of the stuff and sun bake it. It was terribly fragile when finished though.
Clay can be pretty pesky when you find it out in the wilderness. Another problem is that it can contain tiny rocks and stuff that will cause the pottery to be fragile and/or explode in the kiln. The expensive stuff you get at clay shops is the real deal, clean stuff easy to work with (but not cheap per pound). The stuff you may see at art stores and what-not are usually clays that won't dry out,
Sculpey/
Super Sculpey is a good alternative for clay if you don't like all the mess [polymer clays].
Best thing is to bring a big ol' bucket and sieve, then spend some time sifting the clay of foreign particles in some water. Put a trash bag over the bucket and let it take some of the excess moisture out, might take a few days or even a week depending on the consistency (or else you'll be working with mud soup which is totally useless unless you need 'slip').
What you probably made was close enough to "greenware" which is just dried clay, even the better clay you can get is fragile when it's in this state. I lost an entire jug I made in a clay course because the room it was drying in was too humid, stuff happens with clay; people think it's straight forward but it requires a lot of thinking out.