You need to use SMTP auth with a Kerio server, Kerio is not Exchange. Whether or not authentication is required depends on your Kerio settings.
This browser or its version is not supported. Supported browsers: Microsoft Edge 12 and newer; Internet Explorer 11; Firefox 35 and newer; Safari 8 and newer. Kerio Connect, formerly known as Kerio MailServer, was developed by Kerio Technologies based out of San Jose, California. Adopted by thousands of users, Kerio Connect is an SMTP based mail server with features such as global address book, and folder sharing. Because it supports multiple platforms such as Windows, Apple Mac, and Linux, Kerio Connect is a popular choice among small businesses.
Check the SMTP Server configuration on your Kerio server for the correct config to use. If you are permitting relay for an IP group, and your Spiceworks box is in that IP Group, then you should not need to authenticate (but this is a very BAD idea, IMHO). Instead, you will want to check the box to allow relay for 'Users authenticated through SMTP for outgoing mail' and make sure you have created a Kerio account that is dedicated to Spiceworks. In Spiceworks email settings, check the 'Requires authentication' box and enter the username & password of the Kerio account you created for Spiceworks.
I currently use Spiceworks with a Kerio Connect 7.3.2 server and have been since we were running Kerio Mailserver 5.something. It does work, if you make sure the backend settings are there. Let me know if you need any additional assistance on configuring with Kerio!