The Elephants beat the Black Stars of Ghana 3-1 but the display by South African ref Jerome Damon upset Ivory Coast coach Vahid Halilhodzic.
Damon sent off defender Emmanuel Eboue for a reckless tackle on Agyemang Opoku in the 56th minute and gave the stoppage-time penalty when Bamba brushed Asamoah Gyan.
"I'm really angry against the refereeing," Halilhodzic said. "It's too much now. We are going to discuss the matter with the federation's officials to see what we can do about this."
Halilhodzic had also been frustrated when Chelsea striker Didier Drogba was denied a penalty in the 0-0 draw with Burkina Faso.
But the Ivory Coast still became the first team to qualify for the quarter-finals of the event in Angola.
On a poor pitch in Cabinda, Gervinho finished off a fluid counter-attacking move after 23 minutes to give Ivory Coast the lead but Eboue's red card for a two-footed tackle gave Ghana some hope.
Matthew Amoah then struck a post as the Black Stars came close to an equaliser.
Tiene netted a stunning left-footed free-kick after 66 minutes to put the Elephants two up and Didier Drogba headed in a 90th-minute third.
Gyan converted Ghana's penalty with the last kick of the game.