The current Gallery of applications on Azure Websites has a limit number of apps that can be installed out-of-the-box. This means that a long list of appscannot be installed directly from the Azure App Gallery.
To get around this, the current solution is to install these apps on their own Virtual Machine. A Virtual Machine (VM) image for Magento is posted by the Microsoft Open Technology team can be found.
However, having a dedicated VM means that you need to consider the maintenance that comes with it, the security of the VM, and many other factors that makes VMs cost more to maintain than Azure Websites.