You ideally need to set a router as part of your component. The menu manager will override the component/myapp bit, but what comes after that will be determined by what is in the router.php file.
http://docs.joomla.org/Supporting_SEF_URLs_in_your_component
If, however, you simply need to create a link to a specific menu item, then you can always just add an Itemid to your parameter
JRoute::_('index.php?Itemid=12')
will point to any menu item with the id 12, so if that is your menu item ID for your com_myapp component, it will create the menu version of the link to that page.
edit:
You could technically assign the same component to two menu items, so I don't believe that handling the beginning of the URL is default behaviour when you link to a component outside of a menu item without giving the link an itemid. Joomla say (on creating a link for JRoute)...
"Notice that it is possible to leave out the parameters option and
Itemid. option defaults to the name of the component currently being
executed, and Itemid defaults to the current menu item's ID."
ie, call it from your homepage (or any page outside of one set to use your component) without an itemid or option and it is likely to think you are in com_content and with the homepage menu item.
If you want to link to the component outside of a menu item but without hard-coding an itemid, then one way would be to add a Menuitem field type to the config options of the module or template where you are linking from, and then add the itemid it generates to your link.
You could also use JFactory::getApplication()->getMenu() to find which menu item is linking to your component. Not had chance to test this - but using that could also mean that you can set an itemid parameter in your router.