The 25-year-old was in action when Ghana suffered a disappointing 2-1 defeat at the hands of the Blue Sharks at the Felix Houphouet Boigny Stadium on Sunday.
Goals from Jamiro Monteiro and Garry Rodrigues were enough to see the Island nation claim a surprise win in their opening Group B game.
Ghanaians have been very critical of the Black Stars, with some even calling for some players to be dropped in the next game.
Addressing journalists in the aftermath of the game against Cape Verde, Mensah admitted the pressure that comes with playing for Ghana.
The Auxerre left-back expressed his disappointment, insisting the players are aware that everyone expects them to win every game.
“This is not how we wanted to start the tournament. We have another game and we can make ourselves proud,” he told sports journalist Owuraku Ampofo.
“We play for a country where everyone is expecting us to win every game. We’re going in with the same pressure and the same hunger.”
Ghana will face Egypt in their next group-stage match on Thursday, January 18.