You need to add a client Web Part, but doing the following:
"Right-click the SharePoint Add-in project (not the web application project), and then choose Add > New Item > Office/SharePoint > Client Web Part (Host Web). ("Client Web Part" is another name for "add-in part".)"
(reference: https://msdn.microsoft.com/en-us/library/office/fp179921.aspx)
While the example is for a ASP Forms project, it seems to work just as well for an MVC project. You can either create a new web page (view) or point to an existing one (the reference is controlled by the element.xml)
"< Content Type="html" Src="~remoteAppUrl/ClientWebPartPage?{StandardTokens}" / >"