The issue you are running into is partially an HTML issue. Forms cannot be nested. You are likely putting this inside of another form (as a great bulk of the backend is already forms).
WordPress provides good handling for receiving submitted data to extend core functionality. I suggest that you look into this and figure out how to capture the data from those fields when the form is submitted and do what you wish with it from there.
See: https://stackoverflow.com/questions/379610/can-you-nest-html-forms