Note - Dispensador's link isn't to OED, it's to Oxford Dictionaries online (someone else can explain how that relates to OED, which I'm afraid still requires a subscription to access).
Anyway, I did my Lit Crit studies 40 years ago, so I didn't quite get exposed to this relatively recent usage at the time. But here are the relevant bits from the "real" OED...
analeptic, adj. and n.
Sense 2: Literary Criticism. Of the nature of an analepsis or flashback.
Sense 4: Literary Criticism. The narration of an event at a point later than its chronological place in a story; an instance of this, a flashback. Cf. prolepsis.
You can look up (non-medical! :) prolepsis there - it's all just more about with narrative, syntax, and other Lit Crit stuff.
Armed with the information above, it should be reasonably clear that OP's original use of the noun form was at the very least "inelegant" (replacing analepsis by flashback produces nonsense).
Sadly for OP's teacher, I must report that OED doesn't list this figurative Lit Crit usage under the more explicitly adjectival form analeptical. As indicated above, it's new to me. But here's my take...
We're looking at something like the electric/electrical distinction. OED says both analeptic and analeptical are valid adjectives, but the second is only used in the literal medical sense. Therefore the stylistically and grammatically preferred rephrasing should be (drumroll! :) ...
The cellist's music inspires analeptic moments for the characters.
TL;DR: The teacher is more right than OP. Analepsis is a noun like allegory, imagery, paradox. It's a characteristic of (or device used within) a narrative, not something that can be "inspired" in the characters within the narrative.
But the dictionary makes it clear analeptic (not analeptical) is the correct Lit Crit adjective.