VPN Establishment capability from a Remote Desktop is disabled
To get this to work you'll probably want the latest Any Connect client, and you'll need to modify the Any Connect Profile.tmpl file. The file can be found on your machine (once the client is installed). It's an XML-based file, and contains a setting called 'Windows VPNE establishments'. Modify the setting to say 'Allow Remote Users' instead of 'Local Users Only'.
You may be able to save the file and connect without a problem. However, I had to push the modified template from the ASA to the client to get it working properly. When you've modified the Any Connect Profile.tmpl with the necessary changes, upload that modified file to the ASA using the CLI (tftp) or ASDM. A good place is just "disk0:/Any Connect Profile.tmpl".
In the web vpn con fig mode, create a new profile using that file.