Yes, rinse well. With a rug this size you can do a better job outside with a garden hose than you could ever do with a carpet machine (which are basically just a vacuum, and will leave some residue). Rinse with a strong jet 'til the water runs clear, with no soap bubbles.
Also, the beater brushes in the carpet machine can cause pilling.
What's it made of? If it's synthetic it probably doesn't matter much what soap you use, but if it's wool you definitely want to be careful. For the former, I've used plain dish soap, and for the latter, baby shampoo.