I made an App Service (S1) and then from the Networking blade created a VNet Integration using the documentation here. The connection looks like 
Then I made a Storage Account and under the Firewall and Networking tab I selected the preconfigured VNet that was made by the portal 
Trying to access the Azure Storage from a deployed Web App give a 403 forbidden error. What settings do I need to change for the Web App to gain access to the Azure Storage Service Endpoint?
Vnet integration gives your web app access to resources in your virtual network but does not grant private access to your web app from the virtual network.
Private site access refers to making your app only accessible from a private network such as from within an Azure virtual network. Private site access is only available with an ASE configured with an Internal Load Balancer (ILB).
More information about ILB ASE, please refer to this article.
来源：https://stackoverflow.com/questions/49550931/app-service-vnet-integration-with-azure-storage-service-endpoint