This is because you placed the menu on a template-generated page with no editable region for the header, it didn't have any place it could put it.
If you create a template in DW it will automatically create an editable region in the header so that this problem won't occur when adding code that requires header updates. Somehow it was removed for your page either on purpose or by accident or this was a template created in a much older version of DW.
If the editable region was there it would have added the code in the correct place. So it isn't that you did something wrong when you applied as much as it is that the template you are using won't lend itself well to anything that uses external .js and/or .css like menu writer requires.