I'm generally okay with Shinji Kagawa operating off the flank in attack as an interiore (a nominal wide attacker that drifts around laterally in the space between the opposition's defensive and midfield lines), however, I still prefer him in a central playmaker's role*. If you watch Japan, though, it's pretty clear why he needs to be shunted out to the left for them: he and Keisuke Honda are their two most creative players but the CSKA Moscow playmaker is immobile -- or it's more that he simply chooses to never move. Thus, the more (willingly) mobile and versatile Kagawa is able to accommodate Honda by moving out wide in the attacking-midfield band of Japan's 4-2-3-1.
* Don't worry, Kagawa out wide to the left won't reduce me to tears like it does to Jurgen Klopp.
There is one major inherent weakness to deploying an interiore: because they constantly drift into central ares, or even onto the other side of the pitch at times, the space on the flank that they vacate can be badly exposed by an opposing attack-minded full-back. In Brazil's case, they deployed the world's most dangerous attacking right-back in Dani Alves against Kagawa. This left Japan exposed.
While Alves definitely got forward plenty, he actually did sit back a bit more than usual -- at least in comparison to when he's in a FC Barcelona shirt. This very well could have been because he was instructed to be cautious against Japan's most dangerous attacker in Kagawa or it's that he was pinned back somewhat.
Kagawa's role was pretty clear: Brazil dominated possession (somewhat surprisingly) , but when Japan won the ball, they looked to find Kagawa in central areas and from here, the Manchester United playmaker was to ignite counterattacks. At times, he did this well and he had a nice moment in the 9th minute when he received the ball fairly deep, skipped past a few challenges in midfield, before he released a fellow attacker into space in the final third. As the game wore on in the first-half, though, the 24-year-old increasingly came deeper and deeper for the ball because Japan's attack was starved of service -- this also increasingly moved him farther away from his initial position on the left-side of attack.
As mentioned, Alves wasn't positioned as far forward as he usually is for Barcelona. His starting positions were deeper and in this area, he had plenty of time on the ball because of Kagawa's central and deep positions. He also had plenty of space to drive foward into. The result of this was the Brazilian right-back having more touches on the ball (123) and passes completed (84) than anyone else in the match. In addition, on Brazil's second goal, it was Kagawa that got sucked into a central position and when the ball got switched out to Brazil's right-side, Japan left-back Yuto Nagamoto was forced to deal with both Hulk and Alves -- when Hulk darted inside, this freed up just enough space for Alves to whip in an uncontested cross that ended up being an assist.
It should be pointed out that that there's a decent chance Kagawa was designed to be given a free role in attack, and thus, him leaving Alves free so often might not have been entirely his fault. Nagamoto was definitely leaving Hulk at times to his center-backs and central-midfielders when Alves was bombing forward, therefore, the Japan left-back was exhibiting a focus to look for the Brazilian right-back's forward runs. Had Japan controlled the ball a bit better in this game, Kagawa would have had more opportunity to stamp his creative authority on the match. The way the match was though, Brazil dominated both possession and more importantly, the territory battle and this far too often provided Alves attacking opportunities. Because of Japan's strategy to use Kagawa the way they did, and because of their failure to play better against Brazil, this compounded Kagawa's vulnerability as an interiore.
One quick note on Honda: in the past, United have been loosely linked with the playmaker -- I say 'no thanks' to this possibility. He can be dangerous when he receives the ball at his feet and on set-pieces, however, he's far too static for me.