The story doesn't define him as asexual. It does say he scorned and mocked people who then cursed him:
‘So may he himself love, and so may he fail to command what he loves!’
https://ovid.lib.virginia.edu/trans/Metamorph3.htm#476975711
Also according to this article at Cornell, Ovid was the sole poet of the story and there aren't any earlier versions, so it is likely both of our interpretations are askew.
https://www.cornellcollege.edu/classical_studies/CLA216-2-A/narcissus-echo/
Ovid was a Roman not a Greek.