Hi Johnplizarazo
First, I'm not very familiar with azure more aws...
Then i would ask what type of vpn do you have? Policy based vpn or route based vpn?
On route based vpn, you can add a default route going through tunnel interface.
On policy based vpn, you have to do a full tunnel which means on your crypto acl, you need to add the 0.0.0.0/0 statement.
Then for both of them, the traffic arrives on outside interface and i bet you're using the same interface to access Internet, am i right?
If so you need to allow traffic coming in and going out the same interface using the command same-security-traffic permit intra-interface. Then you'll need to nat this traffic and for this you'll need to do u-turn nat config. Afterwards, adapt your ACLs if needed to allow them accessing internet.
After these changes on your asa, you'll be able to access Internet from azure.
Thanks
Francesco
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