Egyptian Mahmoud El Gohary (1959 and 1998) is the only other individual to have achieved the feat.
"When I came on board a year and a half ago my dream was to make Nigerians happy that they could have a very good team they could be proud of," a beaming Keshi told reporters. "We are not there yet but we are in the process and I am happy about that.
"I am so proud of what my players did in this tournament, they played well and they concentrated on the job. They have so much potential."
Sunday Mba scored the only goal in the 40th minute and Keshi joked that he could not describe what he was feeling in the last few minutes of the match.
Nigeria had to weather a late Burkina Faso onslaught before winning the trophy for the third time.
Uppermost in Keshi's mind was the fact Burkina Faso equalised with the last kick of the game when the two sides drew 1-1 in their opening group game three weeks ago.
"You don't want to know what was going on in my head five minutes from the end," said the Nigeria coach, laughing loudly. "So many things were going through my head but I was keeping the faith."
Keshi was under huge pressure to win the tournament, almost two decades after he captained the country to their last Nations Cup triumph in 1994.
The Nigerian media had been scathing of his decision to leave established players like Peter Odemwingie and Obafemi Martins out of the squad in favour of younger, inexperienced players like match-winner Mba who plays in the domestic league.
Nigeria's victory means they will now face world and European champions Spain, Uruguay and Tahiti at the Confederations Cup in Brazil in June.
"It is an honour for us as Nigerians to represent Africa," said Keshi. "I haven't even thought about it yet but it gives us the chance to continue to improve."