"Perhaps we were tired in the final but I don't want to make excuses," Put told reporters. "I saw my team fighting to the last minute - I'm very proud and all Burkinabe can be proud of these players.
"We played a great tournament. No one was expecting us to achieve these results," he added of a fairytale run to a first Nations Cup final that included eliminating holders Zambia and beating Ghana on penalties in Wednesday's semi-final.
Sunday's match was the sixth for both teams in the space of three weeks and was decided by a 40th-minute goal from Sunday Mba.
The Belgian-born Put said he would now talk to the Burkinabe soccer federation and the government about getting more financial support for his team as they bid to qualify for the 2014 World Cup in Brazil.
Burkina Faso are back in action in six weeks' time with a World Cup qualifier against Niger at home in Ouagadougou.
"We've had a great tournament and a massive experience to play in a final in a stadium like this," said captain Charles Kabore of the 80,000-capacity Soccer City venue.
"Nigeria proved a great team with strong mental ability. We have no regrets," added the Olympique Marseille midfielder who was one of the best players in the tournament.
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