The incident in their 1-0 win barely caused a ripple at the tournament, a stark contrast to the wave of outrage which swept the continent when a handball by Uruguay's Luis Suarez denied Ghana a place at the 2010 World Cup semi-finals.
On that occasion, Suarez was vilified after punching away a goal-bound shot on the line deep into extra-time of the quarter-final which the South Americans won on penalties after a 1-1 draw.
Mensah, who had scored Ghana's goal earlier in the match, pushed Jerome Ramatlhakwane from behind on the edge of the area when the Botswanan had a clear run on goal, doing just enough to make him fall.
"We controlled the game until the red card for Mensah," coach Goran Stevanovic told the Ghana FA's website.
"We created some chances but they closed down the game with 10 men behind the ball."
"It's always very difficult to play against opponents who have 11 men behind the ball, which is what Botswana did," striker Asamoah Gyan told the BBC.
"We have a lot experience in this squad and we know what's required of us, and we're determined to make our fans happy."
