Having lost their opening game in Group C to Ivory Coast, Alberto Zaccheroni's men knew that victory in Natal was imperative to give themselves a real chance of qualifying for the knockout stages.
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"We knew that we needed to win two games," Honda told NTV after picking up the man of the match award. "So, it's disappointing that we couldn't get the ball into the goal.
"The result is everything, so regardless of the attacking performance it is disappointing we couldn't get three points.
"Greece played knowing that with a draw and a win in the next game they can go through, and we got caught up in that. We have to fight until the end and not give up."
Yoshito Okubo was just as devastated by Japan's failure to turn their dominance into goals.
"It's a disappointing result and I apologise to the fans," he said.
"We had a lot of chances and we could have won if we'd scored one of those. We had a lot of possession in Greece's half, so we just have to work harder at putting the ball in the back of the net."
Atsuto Uchida confessed that Japan only had themselves to blame but insisted that they will rouse themselves for their final group fixture against the Colombians.
"Football is about scoring goals," he acknowledged. "But, representing Japan, we can't give up on the pitch, so we have to keep fighting."