I have found two different approaches for this, depending on what you're trying to see. The list you created in the sharepoint app is in the app web, not the host web, so it makes sense that you can't see it in the host web contents.
To view lists, files and folders in your app structure, you can use the sharepoint REST api in the browser. This will return an xml of whatever you searched for. Here is a link to this documentation. For example, if you want to see the items in a list, your query would look like:
For site columns and content types, you can steal the query stucture from the developer site. For example, if you can see your host web's site columns using
http://devsite/_layouts/15/mngfield.aspx, you can see your app web site columns using
Unfortunately this doesn't work for me when trying to look at all the site's lists (I get a 403). However, you can get a native list view of a specific list using a standard url. For example, to see a list called Tutorials which is in your app web, you would browse to