The supporter eluded security at Cape Town's Green Point Stadium and went into the changing room after the match with the players and officials but, according to Beckham, did not insult or harangue them after the team's awful performance.
Beckham, speaking at a reception in Johannesburg hosted by Prince William, the president of the English FA, on Saturday said: "It has been blown out of proportion.
"The fan just walked in very casually and just said something to me and then walked out.
"There was no scuffle, there was no aggression at all.
"He didn't comment on the performance. He just walked in, said 'hello'." Prince William, who along with his brother Prince Harry watched the Group C match before going to the dressing room but had left just before the fan arrived, said: "Harry and I had left the door open, it was our fault."
POOR START
Beckham, who cannot play in the World Cup because of an injury sustained before the tournament, has been involved in the England squad as part-mentor to the players and part-ambassador for the country's bid to host the World Cup in 2018.
He said his England team-mates can still recover from a poor start to the tournament and advance to the knockout stages.
"If we win our next game we win the group. We know we've not played well in the first two games but we haven't lost and we've got the two points. We can get it back on track, maybe win our last game and it's looking good again."
England can reach the second round by beating Slovenia, who are top with four points, in their final group game on Wednesday when the United States, who are on two points, play Algeria.
Beckham also thanked England's passionate fans, many who felt so aggrieved by the abject performance against Algeria that the boos and jeers were heard above the din of the vuvuzelas.
"The fans are incredible. They've supported us everywhere in the world and will continue to do that. Hopefully, we can win this game and then go through and start enjoying it," he said.
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