First off lets just talk basic geography. The atlantic ocean can be crossed in about 5,980.32 km ( taking the distance Ben Lecomte swam ) and the Pacific is 14,500 km ( granted these distances may be exaggerated since there isn't a uniform measurement here, but you get the point, the Pacific is huge. The Pacific is about twice as big as the Atlantic. This would be the first barrier to reaching the Pacific, not to mention for there to be any progress you would need to be able to go back and forth, something that is incredibly hard to do.

I'll focus on China first. The Chinese ships were not capable of traveling the pacific in any meaningful way ( read being able to get back reliably ) until well into the 16th century. Up until the Ming dynasty there was never really the ability to go abroad. However, the 16th Century Ming dynasty did technically have ships capable of traveling the Pacific (Look up the ship Free China if interested, it was a Junk sailed across the Pacific in the 20th Century ). The main issue with the Chinese exploring is that they didn't want to. Zheng He did do some exploring, but to the Chinese the Pacific was a vast wasteland of water with uncertain trade benefits. Anything that the new world could have offered them was unnecessary to the Chinese. The Chinese had plenty of wealth and resources, and anything they did not have could be easily gained by trade with India and the Middle East. It is also important to remember the Chinese attitude. The Chinese were called the Middle Kingdom for a reason, they viewed themselves as the center of the universe and everything else just outskirts, thus this disincentive exploration to the East. The Europeans crossed the Atlantic trying to find a way to India, not for any other reason. The Chinese were not desperate to get their hands on European goods, so they felt no need to work hard to try and find a way. The Ming Dynasty had one of the largest navies at the time and surely could have tried, but for them the simple cost-benefit analysis didn't incentive them. It was simpler to trade with India and the Middle East.

For other east asian nations, no one really had the ability to even try. Japan was stuck in the Sengoku (warring) period and did not have the internet stability to attempt exploration, which is an expensive prospect with only minute chances of success. The Koreans focused more on internal development of culture rather than external pressures, not to mention occasionally fighting off the Japanese.

Sorry for any typos, english is not my native language, let me know if there are any follow up questions.

TLDR: China had no reason to, they didn't see any benefit in trying and the rest weren't stable/rich enough to try.