By default the web app server will create a local user which will be used to run the web app server. Local users on Windows don't have access to the network as well as limited access to other parts of the OS.
To get around this permissions issue, you would need to run the web server as a user having more permissions, typically a domain user:
--> Start MATLAB web server.
--> Open the "Windows Services" application
--> Find the MATLAB Web Apps service
--> Right-click and select Properties
--> Under "Log On" tab select "This Account", enter the domain user credentials and hit "Ok" button
--> Finally, restart the MATLAB web server by clicking "Stop" and then "Start" button
The application should now be able to access the Network Drives.