References to pieces of music are generally only as precise as they need to be - if someone wrote lots of Nocturnes we might need to specify the key, or if there is more than one in that key a catalog number. Where a work is unique or far more famous than other similar works we often omit these details. It's up to you to decide really.
The guidance is that the first time you mention it, you should give it the whole title, thereafter, you may shorten it to Clara Schumann's Nocturne (or the/her Nocturne, etc. where the context allows.)
Some refer to pieces by their type, op., and # (Scherzo Opus [...], Number [...]). For example, Chopin Nocturne op. 9 no. 2, but this type of format is more common in music books–e.g., Urtext: Chopin: Etüden: Etudes, by G.Henle Verlag.
Note: Chopin wrote many Nocturne and Scherzo so they are all (mostly) labeled with Major/Minor/Sharp/Flat with note A-G or by Opus and Number. Glasguensis makes an excellent point, but it is up to you... to whom you are writing.