Veron landed a corner close to the penalty area from where unmarked defender Gabriel Heinze powered a diving header into the roof of the net in the sixth minute.
"Diego prepared (the move) and we practised (with Heinze) for a couple of hours," the 35-year-old, who also played in the 2002 finals, told reporters after Saturday's Group B win at Ellis Park in Johannesburg.
"(Nigeria) mark in zone but bunched inside (the box) leaving a very big hole (near the edge). And it came off at the first attempt.
"El Gringo (Heinze) did very well," said Veron, who must get over a minor leg muscle injury if he is to line up against South Korea in Argentina's second match at Soccer City on Thursday.
"We'll do everything we can so I can be there (against South Korea). I think I'll make it," said Veron, who came off 16 minutes from time on Saturday.
He added: "This is not a time to take risks but anyone can (take my place) and do it well."
The inexperienced Javier Pastore, with one cap to Veron's 71, would be his likely replacement although Maxi Rodriguez was his substitute on Saturday.
Veron, who did not have one of his better games for Argentina, said the 1,600 metres altitude of Johannesburg had a bearing.
"For me, the altitude has a big effect, above all on long balls," said Veron, who specialises in long range passes.
"You have to be very precise and that's why we played few long balls. We played (short) to feet because it's a lot easier and above because of the type of players (Argentina have)."
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