Sigil not saving media as part of EPUB

I have an HTML file in one folder, incorporating media files which are in another folder.

When I open the HTML file with Sigil (or Firefox), everything works fine and the files (audio or images) show up where and as expected. However, when I save the file as an EPUB (or EPUB3), the resulting EPUB seems to include only the HTML part, and doesn't incorporate the media files. I can reopen it correctly in Sigil, but if I want to use a copy of the EPUB in, for example, my Android tablet, the media files are, obviously, missing.

There must be a simple solution to this, but my searches came up with nothing.

Thanks.