Griezmann was introduced by France coach Didier Deschamps just after the hour mark in the Europeans' round of 16 victory in Brasilia and the Real Sociedad attacking midfielder added much-needed "mobility and pace" to his team.
The score was 0-0 when Griezmann replaced Olivier Giroud and the former helped lift France's intensity, as they eventually won by two goals to reach the quarter-finals of the FIFA World Cup.
Griezmann played a key role in his team's second goal, putting the pressure on Nigeria captain Joseph Yobo, who conceded an own goal.
The 23-year-old was pleased with how he helped France to victory, as he made his fourth appearance at the World Cup finals.
"I tried to help the team by playing one-touch passes," Griezmann told FIFA.com.
"I'm happy with my performance. You could see in the first half that it was difficult to get behind them but it was better after the break.
"When I came on, I made runs in behind the defence. The rest of the team had worn their defence down well before I came on."
Deschamps hailed Griezmann's impact as well but brushed off comments that he perhaps should have started the Spain-based winger instead of Giroud.
Griezmann started France's first and third group games versus Honduras and Ecuador, while Giroud started the second against Switzerland and the clash with Nigeria at the Estadio Nacional de Brasilia.
"I could have gone with that option from the start and maybe it would have worked and maybe it wouldn't," Deschamps said.
"Instead, I decided to have a target man in the middle, with Olivier Giroud fighting for balls in the air against their defence. Antoine has other qualities, obviously – lots of mobility and pace."
Deschamps added: "It's the game I was expecting against Nigeria, who have a real physical presence.
"We had to be able to meet that challenge for the first hour, then in the last half an hour make more use of our pace and dynamism.
"We took advantage of the fact that the four Nigerian forwards defended a little less in the last 20 minutes."
France will face Germany in the quarter-finals on Friday at the Maracana.
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