Facebook Inc.'s stock price plumbed a new low Thursday as early investors were freed to sell some of their stakes, leaving the once-prized stock down nearly 50% from its debut and forcing executives of the young Internet giant to pump up morale.

Facebook Chief Executive Mark Zuckerberg is no longer brushing off concern about his company's sinking stock price, acknowledging to employees for the first time that the selloff could hurt them.

Mr....