Direct Opposites:
* Discourage
* Dissuade
* Dampen
Words with Similar Meanings but Opposite Effect:
* Suppress (to stop or prevent something from happening)
* Condemn (to criticize strongly)
* Reprimand (to scold or criticize formally)
The best antonym for "exhort" depends on the specific context. For example, if someone is exhorting you to work hard, the opposite might be to discourage you from working hard.