RESOLUTION
You need to enable messaging feature in Virtuozzo Control Center (VZCC) and set up mail relay server.
Please log into VZCC as 'vzagent0' user:
https://Service_VE_IP:4643/vz/cp
Service_VE_IP - IP address of Service VE on a node.
1. Go to 'Configure > Messaging' check this checkbox:
[ ] Enable Email Notifications
and enter required e-mail addresses in 'System Email Account'.
2. Go to 'Hardware Node > Configuration > Email and Notifications' and enter IP address of mail relay server into 'Relay Server IP Address' field.
After that it will be possible to restore password using "Forgot your password?" link.
IP address of email relay server can be set up in /etc/exim/exim.conf file inside Service VE into this section (192.168.32.8 in this example):
# *** DON'T REMOVE/CHANGE this commented section,
# it's need by vzagent to correctly add smart relay to specified address
smart_agent_relay:
driver = manualroute
transport = remote_smtp
route_list = !+local_domains 192.168.32.8 Keywords: VZCC forgot password messaging