dispirited vs downcast

dispirited is not a noun while downcast is a noun.

Word	Noun	Adjective	Verb	Adverb
dispirited	No	Yes	No	No
downcast	Yes	Yes	No	No

As adjectives, dispirited and downcast are synonyms defined as:

Other synonyms of dispirited include blue, depressed, down, down in the mouth, downhearted, gloomy, grim, low-spirited, low.

dispirited (noun)	downcast (noun)
	a ventilation shaft through which air enters a mine

dispirited (adjective)	downcast (adjective)
filled with melancholy and despondency	filled with melancholy and despondency
marked by low spirits; showing no enthusiasm	directed downward