Chim, I have no direct knowledge of the Maytag Neptune, but in general washers do not have filters on the drain line. If they did, you'd have to clean them everytime you do a load just like the lint filter on a dryer. Most likely the material from the rug has either clogged the pump or is interfering with the impeller.
Many years ago I used to work on commercial Speed Queen washers. I've seen bleach bottle caps block the tank drain and many, many baby socks stuck in pumps. I suspect that's the case with your rug material. I doubt that it clogged the hole in the tank where the hose attaches like a bottle cap would, but it probably made it to the pump and then stopped up the works. If you have a sharp bend or crimp in the drain hose, that restricted area could also clog easily.