The meanings of word JUST in english dictionary :
very recently; in the immediate past.
a moment ago, a second ago, a short time ago, very recently, not long ago, lately, only now.
Exactly:
exactly, precisely, absolutely, completely, totally, entirely, perfectly, utterly, wholly, thoroughly, altogether, in every way, in every respect, in all respects, quite.
If you want to argue on those lines:
An adverb is a word that modifies a verb, adjective, another adverb, determiner, noun phrase, clause, or sentence. Adverbs typically express manner, place, time, frequency, degree, level of certainty, etc., answering questions such as how?, in what way?, when?, where?, and to what extent?. This function is called the adverbial function, and may be realised by single words (adverbs) or by multi-word expressions (adverbial phrases and adverbial clauses).
Your "just" has no other verb or adjective to modify, hence makes no sense in actual English.