The goalkeeper pulled off some super stops to keep les Bleus at bay but made a fatal error with 11 minutes left on the clock, failing to clear a corner which allowed Paul Pogba to put Didier Deschamps' men into the lead.
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Joseph Yobo, on his 100th cap, endured the pain of scoring an own goal in the last minute of the match as the Super Eagles failed in their goal to reach the World Cup quarter-finals for the first time in their history.
Keshi openly admitted that Enyeama's error had handed the game to France while hinting that his players taking their eye off the ball is to blame for Nigeria's latest World Cup exit.
"Enyeama had to make a decision and I don't know why he went for it like that," he told reporters. "It's his call and it cost us. It was a big moment.
Keshi also admitted that recent behind-the-scenes protests over Nigeria's World Cup bonuses had been down to "cultural issues", with fellow African nations Ghana and Cameroon also seeing their players go head-to-head with football associations over post-tournament pay-outs.
Nigeria will be heading home from Brazil after the defeat, while France is set to face Germany or Algeria in the last eight.