The Al Ain attacker was not able to beat the Zambian keeper with his spot kick, which would ultimately prove to be costly
Gyan missed an eighth-minute penalty, which was saved by Kennedy Mwenne for the Zambians, who went on to win with a 78th minute goal, a fantastic effort from Emmanuel Mayuka.
It was the second major tournament in which Gyan's penalty miss had proved crucial, after missing another that denied Ghana a place in the semi-final of the 2010 World Cup.
The Al Ain striker has already been at the end of heavy criticism and was mocked on social media for his recent penalty miss.
But Mensah wants encouragement for the player. The Black Stars skipper says Gyan has the backing of the players.
“I spoke to him [Gyan] after the game in the dressing-room. We are all aware that penalties can go either way and it can happen to anyone," Mensah said at a press conference.
“We just have to keep on encouraging him and make sure he can stay fit for the next game."