1962 World Cup, Chile
South Korea made it to the inter-confederation playoff by beating Japan. Much to their bad luck, they had to face a strong Yugoslavia team that ended up making the semifinals in the tournament. Again, no nation from Asia qualified for the World Cup.
1966 World Cup, England
Before the qualification round started, FIFA announced that there will be only 1 qualifying spot for all of Asia, Africa, and Oceania. It was one of the most questionable decisions at that time. Except for North Korea and Australia, everybody chose to boycott the World Cup.
North Korea earned the qualification spot, but there was no chance that they will do anything well. North Korea proceeded to topple Italy and became the first ever Asian team to make it out of their group. They almost caused a second massive shock when leading Portugal 3-0 in the quarterfinals, but unfortunately, Portugal punched back, and North Korea blew the game.
This was the best performance by an Asian country at the FIFA World Cup.
1970 World Cup, Mexico
Israel represented Asia at the World Cup. They were placed in a difficult group with Italy, Bulgaria, and Sweden and as expected they finished last.
Israel had poor relationships with other member countries of AFC, and by the time next World Cup commenced, they were expelled from the Asian federation.
1974 World Cup, West Germany
South Korea lost their inter-confederation playoff match against Australia, and World Cup continued without an Asian team.