Views: add custom no result behavior to a view?
This is not an option in views panes because a 404 should be returned by the page_callback handler, which in this case is the panel that is holding the pane.

Option 1, see if this module works views404, but I have not used it so I do not know for sure.

Option 2, use drupal_not_found(), though I have not tried this in a panel.  Or if you are using contextual filters try this.

Option 3, stop using panels and use view page with Bean and Context and theme regions and a bunch of other things. This way the page_callback is being handled by the view, so the view has the authority to return a 404 instead of theming the frame and other blocks and presenting those.  Downside is you have to restructure the whole site so you probably dont want that.