There is currently no direct service between Panama  and Asia, Australia, Africa, and the Pacific. However, Asian carriers attempt Panama routes from time to time, so this may well change.
Getting to Panama from points east of Europe generally means flying to San Francisco, Los Angeles, or Mexico City and connecting there with Panama-bound flights. It’s usually a quite expensive proposition. Try to find a good travel agent or be prepared to do a fair amount of independent research to find reasonable fares.
Round-the-world tickets or travel using an air pass may prove to be the most economical way to go.