"I'm happy that we accomplished our original goal of reaching the last 16," said the midfielder after the co-hosts second round loss to Turkey.
"But I was very disappointed that we were beaten in the first match of the knock-out round.
"It was a good match, but the result tells us we still have room for improvement. I think we could have gone one more step further.
"It means we still lack something."
Japan and South Korea made history by each scoring their first wins in World Cup finals and going on to qualify for the knock-out stages.
But while Japan's bid to reach the quarter-finals was dashed by the Turks, South Korea sensationally defeated former champions Italy 2-1 on Tuesday.
Parma star Nakata said the Japanese may have been gulity of over-confidence early in the game following wins over Russia and Tunisia and a draw against Belgium in the group stages.
"I think when Turkey scored their goal, we were not concentrating very well.
"But after they took the lead, we started to concentrate, especially in the second half. We played really well. We just couldn't score a goal.
When asked about the next finals in Germany in 2006,, Nakata said: "We've only just finished this one - I just want to take a vacation."