Azure Application not registered with AAD
For me, the easiest way to get everything going was to read the documents from Docker at https://docs.docker.com/cloud/aci-integration/. Really, all you have to do is, create the container in Azure, open up PowerShell(if you haven't, install/import the azure modules,) and run the command "docker login azure." This will pop open a browser window and you can sign directly into your container from there. I haven't tried this with having multiple containers yet, as I only have a need for one so far, but I can't imagine it would be all the difficult.
For those of you who don't want to enable the admin user via the "Access Keys" section in the Container Registry, you can follow this link - https://docs.microsoft.com/en-us/azure/container-registry/container-registry-auth-service-principal - to create a service principal. Running the script provided in the mentioned link generates a ID password combination that can be used with your docker login commands (give the ID as username in the docker login command). This also ensures that if you want to run the docker commands via some scripts that you have written then you can use these credentials.
The command offers the capability of assigning fixed roles to the service principals that you are creating. Roles specific to just pull or push (which includes pull) can be assigned.
The thing that I am not clear about is why don't the users added via the Azure AD can't be used in the docker login commands but using service principals works. (If anyone has an idea about it then please feel free to share).
Go to Access Keys in Container Registry and enable the admin user, then use the autogenerated credentials to login via Docker