Copy and pasting my response to this question somewhere else with minor revisions...
I'd have to say that Western dominance wasn't actually guaranteed until some point in the 18th century. It was still not a given for much of that century that the West would be able to militarily take places such as India. Economically, China was running rings around the West, Indians such as Tippu Sultan presented a credible military challenge to Western nations in India, and the Ottoman Empire was awaking to the challenge that Western modes of organization presented.
To say that European methods were unquestionably superior from very early on are ridiculous to say the least. Until the 13th century, Europe was unorganized and backwards outside of the Eastern Roman Empire, with cities struggling to break 10,000 inhabitants at a time when many cities in the Islamic world and China broke the 100,000 mark. Gunpowder was widely adopted in India, the Middle East and elsewhere not so long after Europe adopted it. Indeed, it was a big factor in the rise of empires such as the Mughals and the Ottomans.
I'll note that While Mehmed II and Murad I were both very passionate and very focused on the acquisition of foreign weaponry and the adoption of new strategies and weapons by the 1600s military innovation had been dropped and the Janissaries were still using outdated muskets and pikes, and Spahis still used lances in the worst way possible. They still had fine discipline and military skill which resulted in the near success of the 1683 siege, but nevertheless they were falling behind. Not to mention the 18th century was actually less of a stagnation than the 17th, where the Kaipikulu system of bureaucracy began to completely fall apart. Thanks to specific reforms in the late 17th century some of this was reverted but there were greater institutional issues in the state. It's really important to note there was no printing press in the Ottoman Empire until the 1720s iirc and literacy remained very low compared to places like England and Germany. Also, after an initial boom of population and commerce where the population of the balkans exploded in the 16th century, it shrunk into a third of its zenith size in the 17th with the collapse of the old system and increasing banditry.
Honestly, the 18th century was much better for the Ottomans than the 17th. As for the question at hand, the issue is that many of these regions were usually pretty despotic and unstable places, even the ones which were more modernized, and the mentality simply was not there. It's telling that when local modernization efforts appeared such as al-Afghani, who to me proposed one of the most natural possibilities for a modernizing Islam, he applied what he had learnt from observing the European powers.
To me the mongol invasions were a red herring and it's honestly kind of insulting since a lot of people love blaming Sufis for the "irrationality of Islam"; never-mind the Sufis produced beautiful works and constituted a continuing literary tradition in the face of apocalypse. What is more important is the effects of the Mongol Conquests, namely the continuing instability in the middle east. The arrival of new tribal groups in these regions and the continued massacre of entire urban centers such as by the Timurids or his depopulation of Northern Iraq and destruction of Nestorianism served to essentially destroy the core of the old Islamic world. It's telling that under the Ayyubids there were over 32 madrassahs in Aleppo alone but by the time of the transition from the Turkish to Circassian Mamluks there were hardly any considering how many times Aleppo had been sacked.
Many of these regions, then, suffered from an institutionalized instability that caused them to suffer immensely and refuted dynamism and economic growth necessary for innovation. In other areas, stagnation ensued with the loss of central administration or facilitated banditry. The Black Death also had an immensely negative effect on the main late middle age center of Islam, Egypt, by causing the Mamluks to resort to forcing many peasants into brutally taxing serf labor whilst old urban centers were essentially abandoned by a country which had lost about 35% of its population, analogous to the outcome of the black death in Eastern Europe where it served to escalate, not relax, feudal dues.
The Ottoman system also suffered from an institutional rot and an essential failure; they could not stop conquering and the entire system was based on such. It was not designed for a static state which was the main reason why it had such severe issues following the death of Sulieman. In a lot of ways his own ego and need to conquer things, especially Vienna, was what drove the Empire into a decline from the more dynamic earlier reigns of Murad and Mehmet. It was overstretched and overworked. It's important to remember the Ottoman final goal was not to establish an Ottoman hegemony over one region. It was to conquer the world for Islam; it seems like hyperbole but both Christians and Muslims genuinely believed that the Ottomans would complete the process of Jihad and bring about a final victory over the infidel. As Rome taught us, basing your system on an unsustainable system of conquest to revitalize your economy and propel you forward tends to end in failure, and it's telling that during the 17th century the Ottomans would go on campaigns regardless of whether they would lose or not. They just had to go. It was the Ottoman way.
Really, the shock delivered by the Austrians under Prince Eugene was the main reason behind a massive shift in Ottoman policy away from eternal conquest and finally encouraged a sense of stagnant stability for the state even if it was one where rot continued to exist at every level of administration. The Safavids meanwhile failed mainly because of their succession system (which the Ottomans themselves adopted) that resulted in weak and idiotic heirs, but more deeply it was an institutional crisis owing to the fact that post-Timurid Persia was as much a tribal entity as a sedentary one, with many competing tribes and clans that were increasingly destabilizing central authority. A good ruler like Abbas could get a handle on and even curtail it, but Persia was increasingly starved of good rulers and increasingly trapped between powers greater than it like Russia and the Ottomans. Nader Shah, for example, was not its salvation but a very symptom of the rot, owing his success to murder and civil war and pursuing a reign with a huge amount of conquest and loot but very little of substance to show for it.
What these states require are lasting, stable institutions to encourage growth. Not knick-knacks and do-dads and world-travelling fleets.