That is the old Imperial myth, that's as old as Imperialism itself. It's such a condescending perspective, as the countries from all around the world were just as inventive, and innovative with their technologies. What happened was very subtle. It was simply the fact that the already rich countries had no reason to expand, while European societies had every reason to expand, as their society was in complete tatters compared to Asia. The rise of European society wasn't just accepting innovation, while others declined innovation, no. Europeans just had more of an incentive to use that innovation for personal gains, while societies in Asia had every incentive to use that innovation for inner stability, and stay course for a non-expansionistic policy. I mean we have Europeans using gunpowder to blow each other up, while China used it for public entertainment, pacifying them, by utilizing it for fireworks. Not mention the Indians were better equipped with firearms compared to the Europeans. I mean India invented rockets at the very time the Imperial powers came in, so that right there throws out the idea that other societies were less inventive, or that invention somehow leads to wealth. They were simply more hesitant to utilize that invention to expand, as inner stability was more valuable to them.
Really I don't know how people can justify that idea. Steam engines don't give you wealth. Using the steam engines for the export of resources does. It was only with the railways that Imperial powers were able to export wealth from India. Not to mention the deliberate sabotage from within the country, by playing the political game very intelligently (the same thing happened in South America, and Africa). How can you ignore the deliberate deindustrialization of the India under that Raj? I mean you have state sponsored brutality such as chopping off the thumps of basket weavers, and making steel production illegal so that they can't practice their trade. Imperialism actively sought to close off, tax out, or straight make local industries illegal, thereby increasing wealth as the Imperial powers were able to sell more readily. The same thing happened with China, albeit indirectly, by deliberate sabotage.
How can you ignore the very idea of Nations, and Nationhood being a very corrosive force that has put ruthless competition at the basis of governance, on a scale never before seen?
Innovativeness does not even begin to cut it. I mean if you're going to argue on culture, then you're putting up a silly argument which says almost nothing, but definitely reiterate Europe's superiority in "culture", which is not a new argument. It's the same old argument that's been used by imperial powers to justify their ruthless conquest since the beginning. It isn't just inventiveness that made Imperial powers more powerful, but a shift in perspective that allowed them to both create the state, and utilize authoritative power for economic gains, coupling that with technology that allowed for global reach.
Just as European society was going through what China had gone through 2000 years ago, that being complete inner turmoil resulting in total war producing a centralized state. Just then it was blessed with unprecedented technological capabilities (that was in fact imported from all across the world), coupling that with the ideological stance which burgeoned due to constant conflict within European society. Ok. So here we have that "cultural" advantage, in that European society was just more ruthless than any other country in the world, not just more inventive. Invention means nothing, and does not produce wealth, it's the use of that invention that matters, and admittedly the Imperial powers did use invention to its fullest capabilities.
Asia in general was in a period of decline at that point, a slowing down, because we don't see the activity of Chinese, and Indian merchants in this period we instead see a recession, and any economist would tell you that this is completely normal for a society.
What wasn't normal for these societies, nor was expected, nor seen ever before in history, was an external force, that too coming from across the globe, that actively had the ability to exploit that recession. That force was able to exploit that recession in a way that allowed for the export of wealth by employing global technologies, and introducing a new set of state sponsored ideologies (soft power).