Gabriel Heinze scored on a diving header in the sixth minute, the only one of seven shots on goal Argentina converted in its 1-0 win Saturday.
Heinze took advantage of weak defense to power in his header from 12 yards off Juan Sebastian Veron's corner kick. After that, it was nothing but missed chances.
"The team made good moves, but we ended up suffering. That's the law of soccer," Maradona said. "Thank God we won the game. To begin a World Cup in winning fashion gives you a certain sense of calmness."
The Nigerians struggled for much of the match to contain Messi, and striker Gonzalo Higuain also failed to convert three good chances.
Messi - FIFA's World Player of the Year - posed a threat to the Nigerians all day.
"I felt comfortable," Messi said. "We knew that Argentina had to show its class and I think we did."
After seeing Higuain miss on an early chance, Messi tried a solo effort two minutes later, forcing a flying, one-handed save from goalkeeper Vincent Enyeama. Enyeama then leapt to thwart Messi after he cut in from the sideline and fired a curling strike.
"He was very close to the ball" at all times, Maradona said. "Soccer wouldn't be beautiful without seeing Messi touch the ball."
Enyeama tried to stay upbeat after turning in a great performance himself. "We're not going to kill ourselves. We have two more games to play," he said. "We thank God the score was a little encouraging."
The Argentines almost paid for their squandered chances, as the Nigerians gained confidence in the second half. Taye Taiwo came inches from an equalizer with a low shot that flew just past Sergio Romero's left post, and substitute Kalu Uche then scooped a weak shot over the crossbar from inside the box with eight minutes left.
"Of course, I'm very disappointed," said Nigeria coach Lars Lagerback. "Unfortunately, there was a mistake from our side that created the corner kick. We were sleeping on one of the corners and that was enough. We were punished this time."