Griezmann came off the bench with the game tied at 0-0 on Monday before helping Les Bleus earn a 2-0 victory.
France's reward for beating Nigeria is a quarter-final encounter with fellow European heavyweights Germany.
"I'm happy with my performance," the 23-year-old told FIFA.com. "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."
France meet Germany in Rio de Janeiro on Friday evening.