The players delayed kick-off by more than an hour on Wednesday night (July 25) when the wrong flag was pictured next to their faces on the Hampden Park screen in Glasgow.
The mistake was later rectified and the match against Colombia got under way, with North Korea running out 2-0 winners.
North Korea's coach Sin Ui Gun said after the final whistle: "Our team was not going to participate unless the problem was solved properly.
"Unfortunately it took some time later for the broadcast to be done again properly and we made the decision to go on with the match."
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He added: "Our players cannot be shown especially with other flags, especially the South Korean one. If this matter had not been solved, continuing would have been a nonsense."
London 2012 organisers said in a statement: "Today, ahead of the women's football match at Hampden Park, the South Korean flag was shown on a big screen video package instead of the North Korean flag.
"Clearly that is a mistake, we will apologise to the team and the National Olympic Committee and steps will be taken to ensure this does not happen again."
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