A vocabulary is an abstract collection of words and not any single one of them. It's also singular, and in that context you'd need to use a plural.
You might say I learned a lot of new vocabularies, which would be grammatically correct but would describe a rather unusual situation. It means something completely different than what you're trying to say and would almost always be semantically incorrect. In particular, a vocabulary is more or less an infinite construct, meaning it's impossible to learn "completely" - which also means it's impossible to learn several of them.
The elements of a vocabulary are, as your teacher points out, vocabulary words. These are not infinite, so it is possible to