South Korea captain Park Ji-sung inspired the visitors and left Japan's preparations for South Africa in tatters, with their opening Group E game against Cameroon just three weeks away.
"I asked the (JFA) president if I should continue as coach," Okada told reporters. "He said 'Yes' - so I'll carry on. It's a question of taking responsibility.
"It's not that I have lost confidence. I just asked if he wanted me to stay and warned him he will take a lot of criticism if he sticks with me.
"To lose twice to Korea in one year, I am deeply sorry," Okada added after the Blue Samurai had suffered yet another blow in a stumbling build-up to the World Cup.
Park stunned Japan in the sixth minute with a superb solo goal, bursting past three players before smashing a right-foot shot into the bottom corner from the edge of the penalty box.
Substitute Park Chu-young added an injury-time penalty to complete a deserved victory for the 2002 World Cup semi-finalists in front of a crowd of 57,000 in Saitama.
"We're gaining confidence with every match," said Park Ji-sung. "It was a difficult atmosphere but we kept our focus on attacking.
"I told the players to win their one-on-ones," added the Manchester United midfielder. "Maybe Japan has that mentality too but we were the better team today."
BATTERED CONFIDENCE
The South Koreans take on Greece, Argentina and Nigeria in Group B at the World Cup following final tune-ups against Belarus and co-favourites Spain in Austria.
Japan face the Netherlands and Denmark after Cameroon but first must try to restore their battered confidence with games against England and Ivory Coast in Europe.
"I only saw brief glimpses of a desire not to be beaten," said Japan Football Association (JFA) president Motoaki Inukai.
"You can't win games like that. It's a real disappointment. That sort of a performance won't get anyone excited about the World Cup."
With Okada likely to be subjected to further ridicule over his target of a World Cup semi-final place, South Korea coach Huh Jung-moo kept his feet firmly on the ground.
"The players kept calm and never lost their concentration," said Huh after South Korea had made it 34 wins to Japan's 10 in 62 meetings between the countries.
"There are still areas we can improve on but we can take several plus points from tonight and go to Austria tomorrow and work towards our opening World Cup game with Greece."
