You can do this

1. Apply your filter in the library module,
2. Select all photos
3. Select "File Menu/Export as catalog..."
4. Click "Export selected photos only" (This doesnt export the photos, only the metadata) , uncheck the other checkboxes
5. Choose an appropriate filename for the .lrcat file, save it, (optionally use the .sqlite extension)
6. Open the .lrcat file in a database query tool that understands the sqlite data format, e.g. code: https://github.com/lazierthanthou/sqlite-manager , download: https://addons.mozilla.org/en-US/firefox/addon/sqlite-manager/
7. Extract the filename info from table 'AgLibraryFile' with SELECT basename , extension FROM AgLibraryFile (customize the SQL),
8. save to csv file

(I admit it's a bit involved and awkward, but it gets the job done.)

An even better solution is:

1. Install Jeffrey Friedl's Data Explorer Plugin.
2. Open this Plugin. (File/Plugin Extras/ jfDataExplorer Explore...)
3. Design a search using any criterion
4. Let the plugin search the catalog.
5. In the final dialog box, click "Save-to-tab-separated-values file" button

This way you can export even the weirdest and sophisticated searches. See screenshot attached.