The anxiety was not limited to Japan either. The US--and, I assume, others--was made very nervous by the prospect of a reunified Germany.
In terms of Japan, that sounds more like an issue with the economic growth of Japan during the latter years of the Cold War. From what I've read, the Japanese economy was supposedly on track to surpass the US economy. The general consensus was that Americans should learn Japanese. The Japanese economy took a significant downturn throughout the 90s and have had mostly stagnant growth since. However, Japan is still the 3rd largest economy in the world and a country that punches far above its weight.
Japan's stagnant economy in the 90's was also due to low birth rates. China is facing the same demographic problems Japan did in the 90s.