Mensah and his team-mates travel to Mongomo knowing that defeat could curtail their hopes of reaching the knockout stages after they lost their Group C opener 2-1 to Senegal on Monday - a match that marked Avram Grant's first competitive game as Ghana head coach.
Andre Ayew's 14th-minute penalty put Ghana ahead, but Mama Biram Diouf levelled in the second half before Moussa Sow scored a dramatic injury-time winner.
Centre-back Mensah is adamant that Ghana are not about to push the panic button, though, and believes the four-time champions can bounce back in similar fashion to their 2010 campaign when they reached the final after losing their opening match.
"I don't think any of us are afraid because this is football," Mensah said.
"That [2010] was my first African Cup and Ghana lost 3-1 in the first game. But we were relaxed and we came back to win against Burkina [Faso] and we qualified.
"So I don't think this is a new thing for us. We are just going to keep our calm and think about winning this game."
Winger Christian Atsu was particularly wasteful for Ghana in the Senegal defeat, but the 23-year-old, who is on loan at Everton from Chelsea, insists there will be no personal hangover from the disappointment.
"Nobody goes into a game to miss a chance but these kind of situations happen in games all the time," he said.
"My intention was to score and make all Ghanaians happy but it didn't work like that."
In contrast to Ghana's woe, 1990 champions Algeria - the highest-ranked team in the tournament - started with a 3-1 victory over South Africa.
A spurt of three goals in 16 second-half minutes saw Christian Gourcuff's men come from behind to win.
Gourcuff, though, will not allow his team to rest on their laurels and is particularly wary of the threat of Marseille man Ayew - a player he once had on loan while coach of Ligue 1 side Lorient.
"They have quality players like their captain Andre Ayew whom I know very well in Lorient and as everyone knows, he has lots of qualities and is capable of making the difference," Gourcuff said.
"We are not going to underestimate our opponent. Our objective remains the three points against Ghana to ensure qualification as soon as possible because it will be very difficult against Senegal a few days later."
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