Substitute Alain Traore’s last-gasp equaliser stunned the Super Eagles, who went ahead through Emmanuel Emenike in Group C, but Celtic’s Efe Ambrose was later sent off.
Keshi, who led his country to Africa Cup of Nations glory in 1994, refused to criticise his players and chose to focus on the battles ahead.
“I’m just going to let everything die down tonight, let them sleep off,” he said.
“Tomorrow morning I will pick it up. If I have to go to individuals and talk to them I will do that, if I have to do collectively I will do that.
“But right now I’m not going to blow their head off for this game, this game is gone. The next game is very, very important against Zambia.
“I will take my time to psych them up and bring them back to the best of their ability.”
Burkina Faso ended their wretched winless run at the Africa Cup of Nations – dating back 17 matches to 1998.
Understandably, their Belgium-born coach Paul Put was more enthusiastic about the result, claiming his players have put their country on the map.
“All four teams have one point so everything is open,” he said.
“The performance today showed who Burkina are. We have quality in the team.
“We were missing some key players so I am very proud of what we did. I was confident of getting a point against Nigeria.
“This was a very good result for us and I am looking forward to the second game against Ethiopia.”