Vincent Enyeama produced several saves to deny the superb Lionel Messi
Nigeria boss Lars Lagerback lamented a lapse in set-piece concentration which allowed Argentina to score the only goal in the opening match of Group B.
Gabriel Heinze was unmarked when he headed in Juan Veron's corner in the sixth minute, while Nigeria goalkeeper Vincent Enyeama made several top saves.
"Unfortunately, there was a mistake from our side that created the corner kick," said Swede Lagerback.
"We were sleeping on one of the corners and that was enough. We were punished."
While Argentina's vaunted midfield and forward line were thwarted by an outstanding display by Hapoel Tel-Aviv keeper Enyeama, Nigeria wasted several potential goalscoring opportunities at the other end.
Striker Chinedu Ogbuke Obasi was particularly profligate, while Taye Taiwo and Kalu Uche missed good chances in the second-half.
However, Enyeama is confident the Super Eagles can respond positively in their next game against Greece, who lost 2-0 to South Korea in Port Elizabeth, on 17 June in Bloemfontein.
"We're not going to kill ourselves. We have two more games to play," said the 27-year-old.
"We thank God the score was a little encouraging."
Lionel Messi saluted the display of Enyeama after his performance kept Argentina's forward line at bay for much of the game.
"The goalkeeper was phenomenal," said Messi after the game. "He takes all the credit. We played a great game and created a lot of chances. We just couldn't get the second goal."
Enyeama said he needed to put on the performance of his life to deny Messi a first goal at the tournament.
"It would be my best possible performance playing against the best possible player in the world, so it was my best," Enyeama told a news conference after he was named man of the match.