I believe you will need to configure the following for this to work:
"After your app integrates with your VNet, it uses the same DNS server that your VNet is configured with. By default, your app won't work with Azure DNS Private Zones. To work with Azure DNS Private Zones you need to add the following app settings:
WEBSITE_DNS_SERVER with value 18.104.22.168
WEBSITE_VNET_ROUTE_ALL with value 1
These settings will send all of your outbound calls from your app into your VNet in addition to enabling your app to use Azure DNS private zones."
--I hope this helps. Please do not forget to "Accept the answer" and "Up-Vote" the answer or message(s) that helped you so that it can help others in the community looking for help on similar topics