let down vs fall short

let down and fall short both are verbs.

Word	Noun	Adjective	Verb	Adverb
let down	No	No	Yes	No
fall short	No	No	Yes	No

As verbs, fall short is a hyponym of let down; that is, fall short is a word with a more specific, narrower meaning than let down:

Other hyponyms of let down include betray, fail, come short, disenchant, disillusion.

let down (verb)	fall short (verb)
fail to meet the hopes or expectations of	fail to meet (expectations or standards)
move something or somebody to a lower position