The meeting frustrated Chinese officials wary of Western support for Tibetan independence, observers say.
"China resolutely opposes any foreign country using Tibet to interfere in China's internal affairs," the spokeswoman said in a statement published by China's official Xinhua News Agency.
Obama and the Dalai Lama both encouraged direct dialogue to resolve longstanding differences between Tibetans and the Chinese government.
Tibet is claimed by China as part of its territory.
Last week, U.S. Secretary of State John Kerry named Sarah Sewall, undersecretary of state for human rights, as U.S. special coordinator for Tibet.
Hua said the appointment would cause serious damage to U.S.-China relations.
"We have never recognized and will not recognize in the future the so-called special coordinator for Tibetan issues appointed by the United States," she said.