"They lost. I am very disappointed."
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.