Widgets are completely different than menu items, so I’m having a bit of trouble understanding what the difficult here is. Some sort of exotic plugin, perhaps? Which widget are you trying to add?
Are you using a custom menu for the menu?
Yes, there ought to be. 🙂
In your 3.9 install, in the Widgets section, there is an option to add a Custom Menu to your Sidebar.
To create this Custom Menu, go to Appearance
then Menus
and then on the Menus page, select create a new menu
.
Add what you want to add to this menu and then save it (make sure it is not selected to be a Primary menu).
Go back to that Widgets page and add in that Custom Menu and it -should- show up in the sidebar area.