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Essien, 31, was named as a substitute for all three of Ghana's games as they finished bottom of Group G, with their tournament overshadowed by a number of disciplinary issues.
Kevin-Prince Boateng and Sulley Muntari were sent home prior to the Portugal game after reports of a disagreement with coaching staff.
The Ghanaian FA has since apologised for their team's poor showing -- but it appears their problems are not over.
"I was notified by my technical team that he [Essien] did not warm up, though he was supposed to," Appiah told a news conference in Accra on Wednesday.
"That was some minutes before kick off against Portugal. Due to the urgency of the game, we had to carry on, and after that I reported his conduct to the FA in my report for the necessary action to be taken."