Asia in trouble too...
The rising marginal cost of a barrel affects everyone who purchases any oil-based products. The more efficient economies and those with access to more, less expensive energy will do better. But all those economies aren't located in Asia. One reason why consumption is shifting to Asia is due to the fact that India and China both subsidize oil consumption. This masks the effect of high oil prices to consumers and, so, they have the illusion of economic growth for a little while. But they pay for this in the form of deficits. India recently had to pass on higher oil prices to consumers and, if marginal costs keep rising, it's just the beginning.
There's nothing magical that makes Asian economies immune to the high cost of oil. They're in the problem along with the rest of us. Further, the mythical 'reserves' of the middle east are belied by the rising cost of producing a barrel there. China receives most of its oil from the Middle East and these countries have been notoriously murky about their reserves figures. Saudi Arabia requires $100 oil for its economic stability. Russia is starting to run to stand still on production. At some point, probably now, these prices start to hurt the so-called Asian growth engines. There's really no way out of the depletion trap unless you have large-scale government and industrial programs to rapidly increase efficiency and to transition away from fossil fuel energy sources.
Honestly, that's the only way out. And the longer we wait for large-scale transitions, the more pain we will feel as the marginal costs of fossil energy ratchet ever-higher.