The Killie midfielder threw his shirt away after being replaced by Danny Invincible as the game drew to a close.
Jefferies said the club would deal with the matter internally.
"They told me he threw his shirt away and you don't do that," he said.
"The reason he was taken off was simple. We were under pressure with a lot of corners coming in so we sacrificed him to get Danny on.
"If he looks at that differently then that is his concern. My concern is for the team and the result.
"That's petulance from him and we will deal with that internally."