The phrase "nasty carpet" does not have a commonly accepted meaning as it is an idiomatic expression that does not convey a specific meaning. Full definition
Oh, and I know what you mean about the pet soaked nasty carpet. (theletteredcottage.net)
There was also nasty carpet on the stairs, so we pulled that up, cleaned the stairs and painted them. (amandarappdesign.com)
We just * finally * removed the very old and very nasty carpet in our living room, but I cleaned that thing more than I'd like to admit. (wellnessmama.com)