It doesn't say
Xanathar's Guide to Everything only says what you've already found; that they don't know that you attempted to charm them if they succeed their save. It doesn't say whether the know that you charmed them if they fail their save.
I checked the wording of Words of Terror feature from the College of Whispers bard archetype, which is similar in nature. From XGTE, pg. 16:
If you speak to a humanoid alone for at least 1 minute, you can attempt to seed paranoia in its mind. At the end of the conversation, the target must succeed on a Wisdom saving throw against your spell save DC or be frightened of you or another creature of your choice. The target is frightened in this way for 1 hour, until it is attacked or damaged, or until it witnesses its allies being attacked or damaged.
If the target succeeds on its saving throw, the target has no hint that you tried to frighten it.
Much the same as the wording for Enthralling Performance, and equally as unhelpful for determining what happens if they fail their save regarding whether they know or not.
Arguments for they don't know
If we consider other ways to charm people, specifically the charm person spell and the friends cantrip, both say that they do know. Given that the Enthralling Performance feature does not say this, we could conclude that if it meant for the target to realise, it would have said so, and therefore because the feature doesn't say this, then they do not know.
From charm person (PHB, pg. 221):
When the spell ends, the creature knows it was charmed by you.
From friends (PHB, pg. 244):
When the spell ends, the creature realizes that you used magic to influence its mood and becomes hostile toward you.
However, these two spells are not all at related to the Enthralling Performance class feature and beyond giving a DM a precedence to rule this way, they don't directly inform us on what Enthralling Performance should do.
Furthermore, if the target doesn't know what happened when they succeed a saving throw, it stands to reason that they shouldn't gain knowledge by failing a saving throw. It seems odd that they should gain from failing something, even if there were other effects at play. Of course, this is just a line of reasoning and ultimately doesn't have any backing from the text.
Since the rules don't explicitly tell us, then unless we have a Word of God answer (and I couldn't find a Sage Advice on this) then it'll have to be up to the DM to decide on an interpretation of this feature that makes sense to them.