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If it needs to be communicated then it needs representation in our vocabulary.
I could see Saussure being influenced by Bhartrihari; the later's philosophy of language is clearly idealistic, sure, but there's some vague hint of "a sign is what other signs are not".
And technically we can describe everything we feel; in practice, we won't.
Emotions are like colours, they're part of messy and multidimensional gradients. And, just like you could have a thousand primary words to refer to colours between red and yellow, or saturated red vs. grey, you could also have a thousand words to refer to emotions between hate and fear, or fear and curiosity, or weak vs. strong fear.
However every association between word and meaning is prone to decay. The word itself might fall into disuse, or the meaning might drift away. As such only distinctions that speakers consider meaningful are kept or reinvented. In practice this means that you'll only see a handful of words referring to emotions; their scope will vary quite a bit from language to language, but you'll often see some common patterns, around things humans in general consider meaningful.