Considering that the drain plug is at the very front most part of the tranny, I would say that indeed, you would want the car as level as possible in order to completely drain it. Or...have the rear jacked up. But...it was probably also just very low on fluid.

If you have a small level, you can hold it up to the side of the tranny at the bottom of the drain hole...that will show you how much you ain't getting out due to the angle.

Them oil pumps are the best way to re-fill...but if you don't have one, it is easy to tape a hose to the end of a bottle, and feed it into the filler hole from up under the hood. Then just let gravity do the work. Its a pain to try to squeeze the oil up from the bottle from under the car.

Have fun!
-Matt