The former Huddersfield Town boss has opted to drop the 32-year-old, who was expected to replace the injured Marlon King, from the squad to face Watford due to a lack of "work ethic".
"It makes me very angry," the Birmingham Mail quotes Clark as saying. "I'm not prepared to accept players who don't show the work ethic required. It's about high standards."
Zigic has failed to cement a regular starting spot in the side this season.