Innovation and engineering aren't necessarily the same. It's true that Japan hasn't invented much, but back in the 19th century the most innovative country was Great Britain, yet they lagged the U.S. because American companies could take British ideas and implement them better, thanks to better management and engineering.
Some Japanese inventions: the tunnel diode (but the transistor blew it away), Yagi antennas, the modern form of video tape (every other line is recorded out of phase so the tracks don't interfere with one another, even without any space between tracks, allowing much less tape to be used), the Toyota production system, the blue LED, and the blue LED laser (same guy for both, but he packed up and moved to the U.S. because of a better offer).