How did you look through the pinhole?
If you put it far from your eye you have seen nothing. It is small hole and you have seen one "overexposed" point behind dark card.
If you put the card as close to the eye as possible think of it as another lens in your eye. And the image was already inverted - it was projected on your retina and your brain automatically re-inverted it so up was up and down was down.
There is no way how pinhole projection can not be inverted. There is no reason to make camera lenses that won't invert the image - the drawbacks of design are far more serious that dumping the chip in correct order, see basics of operation of CCD, (digital cameras), turning the film correctly when developping (film cameras) and adding pentamirror ([D]SLRs' viewfinder). Note that waist-level cameras have inverted viewfinder.
OK, there is one, but it is a Heath-Robinsonian solution: Build your camera with pinhole, translucent screen, another pinhole and the film/CMOS/CCD. This way you'll have inverted image on the screen and double-inverted image on the film.
If you want to see the pinhole effect, find a room, cover all windows except for one small hole. The room will be completely dark, except for the projection of the outside world on the wall opposite to the hole. You will be inside the camera obscura.