As a Chinese-American, I often encounter casual racism against the Japanese in my day to day life. This distaste extends to my Korean and even Taiwanese friends. Yet, while studying in Europe, I find Germans are widely admired, though thought somewhat robot-like. I find this disparity interesting. I know generally the Japanese never "apologized" as it were, but I'd like a more detailed breakdown if possible.
I just finished Embracing Defeat by John W. Dower. It doesn't deal with the way the politics were handled between Japan and other Asian nations, but it does talk about the way Japan itself came to deal with its war experience. In excruciating detail actually, I'd fully recommend Dower for the way he deals extensively with not just the halls of power but the actual grass-roots movements of normal people.
Anyway, I'd retell Dower's analysis as follows:
Basically, as Dower describes it, even though many Japanese were shocked and disgusted to learn about the atrocities committed, the victims of Japanese aggression were not something Japanese themselves (specifically the 90% of the population who never left the home islands) needed to emotionally come to term with. The countless Japanese who died in the war was something the survivors needed to emotionally come to terms with. Just as anybody would have to come to terms with losing a friend or loved one, in a way you don't when it's a stranger.
The end result was an inward focus on the Japanese victims. Which did result in a very strong anti-war movement that continues to this day, but also left the road open for a minority of reactionary ultranationalists who wanted to deny Japan had ever done anything bad altogether.
It's my own addition that I think in Europe there was such a loud and vocal voice of the native victims that prevented that kind of inward focus that appeared in Japan. Also, and I don't know too much about it, but you'll find there were and still are issues with dealing with the fallout of WW2 in Europe. You can generally say we've all reconciled, but it was a bumpy road with a lot of dark and nasty episodes.
First of all, the Americans cared very little about non-Western victims of Japanese crimes. The impression you get from Dower is that according to the Americans the most heinous thing the Japanese did was daring to sneak attack Pearl Harbour. As a result the Americans reinforced a view that the war had been solely between Japan and the U.S. which of course the U.S. won, so in the end as per above the only real victims of the war were the Japanese.
Second, Dower is particularly harsh on the case of the U.S. decision to absolve the Japanese Emperor of any and all war guilt. I'm not sure about that issue in itself, as in whether or not the Emperor was guilty, but I am very convinced by Dower in the argument that the way the U.S. went about absolving the Emperor undermined any serious process of dealing with the larger issue of guilt and responsibility for the crimes of Imperial Japan. On a judicial level, it is more accurate to characterise the post-war situation as the Americans asking a small group of Japanese leaders to fall on their sword to safeguard the Emperor, rather than a true investigation of who was responsible and bringing such people to justice. On a societal level, the Americans spend the entire six years of occupation rigidly censoring virtually any discussion on the issue of war guilt, because they wouldn't allow so much as a hint that the Emperor might've bore responsibility. There was in the end no way for those Japanese who wanted to discuss war guilt to do so, as so much as mentioning the only figure who was actually there throughout the whole period and in whose name everything done was supposed to have been done, led to a quick ban by the U.S. censors. And after the occupation was over the moment had really passed.
Third, even before the occupation was over the U.S. did a reverse course. The Japanese who had most strongly resisted the war and the military regime, the communists, were now the enemy. And war criminals were released from prison and quickly recruited in the new goal of ensuring Japan became a bulwark of anti-communism in Asia. Dower includes some truly disgusting quotes of U.S. generals suddenly praising war criminals because at least they were anti-communist.
While I cannot speak about the culture of modern Asia, I can point you towards one of the many key differences that at least partially contributes to this disparity.
After WWII, the allies enforced an extensive denazification campaign in Germany. Besides the well known Nuremburg trials, there was also a large campaign by the German government to hold even low ranking Nazi's responsible for their actions.
Contrastingly, while Japan experienced some military justice, it was mostly directed at people who committed crimes against American forces. For example, the commander of Japanese forces during the Nanking Massacre, Prince Asaka, was pardoned completely. Imagine how different it would have been if someone like Rudolf Hoss, the comandant of Aushwitz, was let go scott free.
Another example of this is the Japanese biological warfare group, Unit 731, who commited horrific germ warfare experiments on POWs and innocent civilians, and was granted immunity by the Americans in exchange for their research. Because the punishment of Japanese war criminals was weak, uneven, and biased against Asian atrocities, the populations of the affected countries never felt that the Japanese experienced justice the way Europeans did.
If I may ask a follow up question, why is it commonly stated that Japan has never apologized? The government has made dozens of formal statements apologizing over the years. It seems that every new Prime Minister has to make a new apology.
Along with what everyone above has said, the nations that primarily have anti-Japanese sentiment (South Korea and China) have not helped Japan telling them where and how they can apologize. There have been times when Japan has apologized, but all of the countries that were ruled by Japan accepted them except South Korea and China.