The Super Eagles dominated for much of the match in Curitiba on Monday, but they were unable to breach the Iranian defence.
Mikel now believes that the Nigerians cannot afford to drop any more points if they want to reach the second round of the tournament.
"Naturally we're disappointed because we know what it means to win your opening match at the World Cup," he told FIFA.com.
"We thought we had a good chance of winning. We created some openings in the first half and I think we deserved to score. Iran kept us at bay, though, and they were well organised at the back.
"We need to raise our game if we want to reach the next round. We prepared very well for this World Cup and we can't afford to drop another point in our remaining games."
Nigeria return to action on Saturday when they face Bosnia-Herzegovina.