"They lost. I am very disappointed."
很 and 非常 have similar meanings and therefore both should be accepted as correct.
They should both be accepted because both can be translated as "very". But be aware that 很 is very weak and often nothing more than a placeholder because some sort of degree adverb is required (which is frequently the case with adjectives). In those cases it shouldn't be translated at all. 非常 is on the other hand is much stronger. It literally "extraordinarily" and is much closer pragmatically speaking to English "very" than 很.
That would indicate a change: You lost hope/became disappointed. If the focus is on the current state of you feeling disappointed (which it sounds like in the English sentence) I would not use 了.