This is a question which comes up with some great regularity, and it's usually either responded to with links at best if at all.

The simplest and most straight-forward answer is this: technological development is by no means a linear, Sid Meier's Civilization style tree of progression. Innovation doesn't occur in a vacuum, and is usually built upon other sturdy foundations for it. It's not a matter of any one peoples lacking the know-how, but a matter of foundation and need. The rich, productive, and manpower saturated nations of both south and east Asia never had an environment where something like the steam engine was really necessary; though that's not too say they were completely devoid of machinery. Circumstances, simply, did not dictate the need for such an apparatus anywhere but Europe.