EDIT: Addition of information, clarification of wording
Before I start on East Asia, I will note that there is much dispute about "feudalism" in European historiography itself. Here's an overview of the history of "feudalism" as a concept, and there are a number of academic books that discredit orthodox conceptions of feudalism, such as Fiefs and Vassals: The Medieval Evidence Reinterpreted by Susan Reynolds.
Regardless of European feudalism, I would definitely hesitate to call Imperial China or dynastic Korea feudal societies (Japan is a topic I know little about). According to Oxford, feudalism is:
The dominant social system in medieval Europe, in which the nobility held lands from the Crown in exchange for military service, and vassals were in turn tenants of the nobles, while the peasants (villeins or serfs) were obliged to live on their lord’s land and give him homage, labour, and a share of the produce, notionally in exchange for military protection.
Let me use the example of the late Joseon Dynasty of Korea to show why it was not at all feudal; my points broadly apply to China, although circumstances were of course different in the two countries. The landlords of Joseon Korea certainly held land, but there was no exchange of land for military aid. People who were granted land by the state were often gongshin, retainers who had accomplished especial merit (or connected to the throne in some way). Otherwise landlords generally acquired land (ostensibly) through purchase.
For instance, dozens of people were made hoseong gongshin^1 in 1604 and divided into three groups depending on how meritorious their service had been. The most meritorious retainers were granted (Korean translation of the Annals of the Joseon Dynasty link, if you can read them):
Ten guards (伴倘), thirteen slaves (奴婢), seven leased slaves (丘史), 150 gyeol of farmland (about 1.5km^2 ), ten silver coins, and a horse from the royal stable (內廐馬)
The second group was granted:
Six guards, nine slaves, four leased slaves, eighty gyeol of farmland (around 0.8km^2 ), seven silver coins, and one horse from the royal stable
The third group, the least meritorious or notable but the most numerous among the hoseong gongshin, was granted
Four guards, seven slaves, two leased slaves, sixty gyeol (around 0.6 km^2 ) of farmland, five silver coins, and one horse from the royal stable
You might notice that the gongshin are not exchanging anything for the land (or, for that matter, any of the other rewards); it's purely the state's gift in return for their previous merit. It's not very feudal, is it? And despite the existence and presence of landlords, shenshi, wulei, and/or other regional powers, actual political power in the provinces was still at least nominally in the hands of non-permanent state-appointed officials - this applies to both China and Korea.
Ever since private armies were largely abolished in 1400, military power in Korea was monopolized by the central state - Joseon Korea had become what we call a Weberian state, and this state of affairs would endure for the rest of the five centuries of the dynasty (This is a good study about it, but I don't believe you have access. Korean articles or studies usually don't show up in non-Korean sites). This meant that generals or admirals were appointed by the state and could be dismissed or reappointed at will. And in general, there was not much of a link to the region a military commander would be serving in and the commander himself. The typical example might be the admiral Yi Sunshin, now a national hero in Korea; he was born in the capital, but served both on land, on the northern border, and at sea in the south. Again, orthodox feudal concepts simply do not properly apply to Joseon Korea. (the Chinese state usually had less of a monopoly on the military)
What I want to say, and what answers the question about central bureaucracy in "feudal" East Asia, is that China and Korea were much more centralized than the term "feudalism" connotes. Civilian governors appointed by the central state and often from some other region of the empire/kingdom had at least some degree of power more or less everywhere. It was similar for military commanders - a classic example might be Yuan Chonghuan, a civilian scholar-official originally from Guangdong, who served as the military commander of a region more than 2500 kilometers to the north. China (and Korea) was, at the very least in theory, a state governed by a developed central bureaucracy. Without its far-reaching power the state simply could not function as it did. Rather like modern states, actually.
All this is a bit basic, honestly. But for everything dealing with post-Tang imperial China, Imperial China 900-1800 by Frederick W. Mote is an amazingly comprehensive source you should go and buy right now. As for Joseon Korea, good sources in English are few and in between (I don't actually know of a comprehensive history of it a la Mote's Imperial China). Everyday Life in Joseon-Era Korea: Economy and Society by Michael D.Shin is less about government or bureaucracy, but it's still good if you want to know more about the period.
^1 These were retainers who had accompanied the fleeing king Seonjo during the Japanese invasions of 1592. The Chinese characters 扈聖工臣 quite simply translate to "meritorious retainers who accompanied His Majesty."