Polyurethane coating is primarily used on wood, as it acts as a water sealant. Drop cloths are designed to protect your carpets while you paint, but it's not unusual to get a few drops on your floor. Polyurethane paint is more difficult to remove than water-based paint, particularly if it has become dried and crusty. However, there are several steps you can take that will help you get that unsightly stain out.
Manually scrub away at the stain with a toothbrush and some soapy water. The stain will typically come right up if it is still wet. Vacuum up what remains and move on to the next step if there's still polyurethane remaining or if it has dried.
Dampen the end of a rag with some acetone and dabble it onto the stain. Acetone is designed to eat away at coatings and is sold as a commercial paint stripper. Let the acetone stand on the stain for a few minutes. You may need to saturate the carpet with acetone if it is a large or particularly stubborn stain.
Pick away at the polyurethane with a paint scraper. Chunks of it should come up off the carpet. Remove any remaining traces of polyurethane with rags. Repeat this process as necessary to fully remove the polyurethane.
Scrub at the polyurethane with a coarse brush. The brush should help tear paint particles off the carpet.
Clean the area with warm water and liquid soap to remove any of the acetone and blot dry. Vacuum the carpet when finished.