Both Don't be discouraged and Don't be disappointed are perfectly natural things to say, and in many contexts they'll effectively mean the same thing - speaker is advising someone to look on the bright side (to find good things in a bad situation). As OP has discovered, the dictionary definitions are somewhat different, but they're obviously closely related. A "defeatist" reaction to finding ...
Your question falsely assumes it's one or the other. A describes the mood or state of the people when they went away because "disappointed" is an adjective, which modifies the noun "people," like one pictures them crestfallen. B describes the manner in which they went away because "disappointedly" is an adverb, which modifies the phrasal verb "went away," like one pictures them leaving looking ...
The difference between "in", "by", and "with" in this context actually depends on the nature or type of disappointment you feel: "Disappointed with" implies that the cause of the disappointment was something basic about the nature or attributes of the thing: I was disappointed with my new toaster. It really didn't toast the bread as well as I hoped. The "with" form is usually used with ...
grammar - Is it disappointed with, in, or by? - English Language ...
If one thinks "disappointed" must be accompanied by at least some tinge of dejection, the lawyer's phrase "agreeably disappointed" will seem oxymoronic -- or the word "agreeably" itself will have to be twisted to mean "not too disagreeably" as you have done with "not too torn up about it".
Usage of "I am agreeably disappointed in" - English Language Learners ...