The VPN headend (ASA or IOS router) probably has a "tunnelall" (no split tunnel) setting and no provision for allowing your tunneled traffic back out to the internet.
That's not something you can modify at the client side. It may have been done at the headend to enhance security. If it's just an oversight, then a search on "cisco ssl vpn split tunnel" will give the administrator any number of how to guides for allowing it.
