Concrete is extremely porous, and if you had a situation where plastic melted into your concrete, you can expect a laborious task in cleaning it up. A heat source had to melt the plastic onto the concrete and you have to use a heat source to clean the plastic back off. According to David Derr, a contractor with over 25 years experience, although it is likely that you may never completely get rid of the plastic, it is possible to remove the plastic that makes the concrete look like an eyesore.
Heat the plastic with a heat gun. Hold the heat gun approximately 10 to 12 inches away from the plastic to avoid overheating it. You do not have to liquefy the plastic -- you simply need to heat the plastic until it is pliable. If you do not have a heat gun, you can use a hair blow dryer. A blow dryer will take longer to heat the plastic.
Scrape the plastic off the concrete with a putty knife.
Reheat the area with the heat gun and remove any excess plastic with the putty knife.
Sand the surface of the concrete with a concrete floor sander. If the area is small or you do not care about inconsistencies in the surface smoothness of the concrete area, you can use a small orbital sander to sand just the area that had the plastic on it. Start with a 60-grit paper and graduate to an 80-grit and then a 100-grit. The only plastic that will remain is the plastic that melted deep into the pores of the concrete.