Broos had goalkeeper Fabrice Ondoa to thank for earning his side a point with a brilliant reaction save from Didier Ndong in second-half injury time, and the Belgian coach praised his players' commitment for the full duration of the game.
Cameroon is likely to face Senegal in their quarter-final, and Broos called upon his side to maintain its performance levels.
"Every game we have played has been against a motivated team who fought to the end," he said. "Now we are qualified and we are very happy. Everything is open.
"Senegal are maybe the best team in the tournament but this is only words. If we play with a big heart like we always do, and have a better beginning of the game and end of the game - not like today - then there will be something great for us in the quarter-final."
Gabon coach Jose Antonio Camacho refused to be drawn on his future after his side became the first host nation to be knocked out of the tournament at the group stage since Tunisia in 1994.
The Panthers drew all three of their group games, but Camacho defended his players' efforts.
"We are very disappointed because we did not qualify. We played with all our heart in every game," he said. "No one can predict the future. It would just be words if we were to try and predict the future.
"The sadness is still very strong so this is not the moment to talk about the future. We have to talk to the players to know if I will continue with them or not."
Camacho admitted his side's preparation for the tournament was inadequate, saying: "We did not have enough time to play friendly matches."