I don't think stamina has ever been an issue with Japan, even when they were there to make up the numbers. The CIV equalizer was the result of a brilliant cross met by an equally brilliant header put together by very good players from a very good team. No stamina issues from what I saw. The game winner was also from an excellent cross but this time met with a header Kawashima should've had.
That said, it's terrible to give up a lead but then again trying to preserve a one goal lead by trying to run out the clock, especially for a team that scores most of its goals on the counterattack, isn't smart.
Japan has tactical issues to address, not anything else IMHO.