This happens because of a new version of the package "ifupdown" which is not compatible with OpenVZ.
If you didn't upgrade this package yet, run the following command before running apt-get upgrade:
echo "ifupdown hold" | dpkg --set-selections
If you already upgraded your system, go to our out-of-band console accessible from our Control Panel and edit /etc/init/networking.conf
Find a line that looks like this:
start on (local-filesystems
and stopped udevtrigger)
and modify it as follows:
start on local-filesystems
After that reboot your VPS.