In most distros sendmail is configure to listen only on the local loopback interface. Run:
netstat -tan|grep 25
and see if it's listening only on 127.0.0.1.
In this case only localhost can use it as a relay to send mail.
You can also use /etc/mail/relay-domains to add the hosts/IPs you want to use your server as a relay.
Another possibility is to use /etc/mail/access to allow relay based on hosts, IPs, the "From:" field, etc