Sierra Leone had needed a point to progress, but 37-year-old striker Kei Kamara saw his 84th-minute penalty kick saved by Jesus Owono.
While Ivory Coast and Equatorial Guinea cruised to the round of 16 with seven and 6 points respectively, Algeria crashed out with one point.
The president urged the Austin Eguavoen-led team to maintain and even surpass the form that made them leaders in the group stage.
“The most credit must go to the players for doing everything we told them to do,” said Eguavoen.
This is the first time in their history that Ghana have failed to progress from the group stage.
Neither side could eventually find the breakthrough as Senegal sailed through, while Guinea joined them despite their loss as runners-up.
Super Eagles have six points from two games, having beaten Egypt and Sudan, while Guinea-Bissau have just one point.
Algeria will go into their last group stage match with a point against group leader Ivory Coast, who have 4 points.
The coach said he would make some changes in the final group match against Guinea-Bissau on Wednesday.
The Super Eagles will take on Guinea Bissau next in their final group game on Wednesday.
