Hi @Harsha Cheruvula ,
Thanks for contacting Microsoft Q&A platform.
It seems like you have successfully installed Cisco AnyConnect VPN on Azure.
There is restriction from Azure to block outbound connectivity to any VPN by default. If you have any outbound NSG rules defined to block the traffic, then make sure you allow outbound traffic to Internet.
It seems like an issue with the Cisco Anyconnect config rather than an issue with the Azure VM. You can check this thread as well for more info.
You can try to post your query on Cisco forum as well here.
Hope it helps!!!