Burkina Faso's 1-0 win over, the already qualified, Mauritania was not enough for the Stallions to qualify for the finals.
The results mean that Angola top the group ahead of Mauritania thanks to the better head-to-head record, with both teams on 12 points.
The duo end the campaign two points ahead of Burkina Faso with Botswana bottom with just a single point.
Wilson Eduardo was the hero for the Palancas Negras as he scored on his debut after swapping national allegiances from Portugal to play for Angola.
Eduardo, whose younger brother Joao Mario plays for Inter Milan and Portugal, scored midway through the first-half.
The match was meant to begin at the same time as Burkina Faso and Mauritania but eventually ended almost 20 minutes later.
Kick-off in Francistown was 10 minutes later than Ouagadogou and floodlight failure at the start of the second-half delayed the game even further.
Burkina Faso got the win that they needed to have any chance of reaching the finals thanks to a goal from Lyon's former Chelsea forward Bertrand Traore after 19 minutes.
They then had to endure a 20 minute hoping for a Botswana equaliser which never came, that would have have seen them qualify for the finals.