Pierre-Emerick Aubameyang and Malick Evouna struck to win the Group A game for the Panthers, although they were also indebted to goalkeeper Didier Ovono for making several vital saves.
"We dominated the first half and created clear chances, but unfortunately Didier Ovono was very strong today and he won the points for Gabon," said Put, who led the Stallions to the final of the 2013 Cup of Nations in South Africa.
"If you can't score goals, you can't win matches. That's the rule of this game. It's a shame, but that's the way it is. In the second half we tried to keep going and had more chances. You need luck and patience in front of goal if you are to score, but that wasn't the case for us."
Gabon, meanwhile, could qualify for the last eight with a win against Congo on Wednesday, when their coach Jorge Costa will be hoping his men once again have luck on their side. "Burkina Faso are the strongest in our group, but today we had the luck and we also had Didier (Ovono), he was decisive for us. We worked hard and had 11 panthers on the pitch," he added. "We are right next to Gabon here and the fans helped us today."