I think you may need to use the functions settings_fields do_settings_sections and register_setting as well as add_setting_section to get this working see refs. to these functions here. I’m not sure if you could get a bare bones version working leaving some of those out but maybe or maybe not … there are a lot of functions used in a working options page I know.
I would advise copying a finshed working options page such as Jeffrey way’s offering into your theme and removing stuff till you get to a bare bones working model. It will help you to understand this as it’s pretty complex.
It’s also complex enough to warrant setting up multiple practice themes on your system so you can experiment with different versions/stages of an options page if it’s your first venture into it.
Also in research be aware of the “Old way” and “New way” of doing settings. Settings API is the “New way”
Edit – as Eric Said, having “administrator” as capability is suspect.