counterfeit vs inauthentic

counterfeit is a noun but inauthentic is not a noun.

Word	Noun	Adjective	Verb	Adverb
counterfeit	Yes	Yes	Yes	No
inauthentic	No	Yes	No	No

counterfeit (noun)	inauthentic (noun)
a copy that is represented as the original

counterfeit (adjective)	inauthentic (adjective)
not genuine; imitating something superior	false or fake; not what it appears to be

counterfeit (verb)	inauthentic (verb)
make a copy of with the intent to deceive