The "Chollima" reached the last eight in England after beating Italy in their group and led Portugal 3-0 before a Eusebio-led fightback saw them exit the tournament 5-3.
"Revenge," An told reporters at the Makhulong stadium. "We want revenge for 1966."
In only their second appearance at a World Cup finals, the North are the lowest ranked team in South Africa at 91 and have been drawn in the "Group of Death" with Brazil, Portugal and Ivory Coast.
Far from being intimidated, however, North Korea are optimistic about their chances of making the second round and striker Jong Tae-se has predicted a shock victory over Brazil in their Group G opener on June 15.
An recognised the strength of the world's top ranked side, but he too thought it as possible the North could take all three points from the five-times winners.
"Brazil are the strongest team in the world, they don't have many weaknesses," said An, who was born in Japan, played club football in South Korea and holds a North Korean passport.
"I've asked my Brazilian team-mates at my club how to beat them. We don't have much of a chance to win but it's not impossible."
Given the fragile relationship between Pyongyang and Seoul following the sinking of a South Korean naval vessel, it is unlikely the South, which has broadcast rights to all of the Korean peninsula, will give free coverage of the games to North Korea.
Fans would still get the chance to see the games, An said.
"I don't know if it will be broadcast live in North Korea but it will be broadcast," he said, adding that he expected to see some North Korean fans in the stadiums.
North Korea will face Ivory Coast in their final group game on June 25, and while An knows that a fit Didier Drogba could run his side ragged, he is eager to face the striker who suffered a broken arm on June 4 in a friendly.
"It would be a real pity if he missed the game. I don't get the chance to play against world-class players very often," said An. "If Drogba plays it will make the game much more difficult but I think of him as a soccer hero."
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
‘England have the players to win the World Cup – it’ll be tough for Thomas Tuchel to do a bad job, with the squad he has at his disposal’ Former Three Lions winger backs new boss after gentle qualifying draw
