Although the Republic of China insisted the succession of the whole Qing Empire, the Mongolians and Tibetans regarded the fall of the Qing Dynasty as the separation of the Empire. This meant that the Manchu Empire was dissolved into China, Mongolia, Tibet and Eastern Turkestan. They concluded the treaty proclaiming the independence of Tibet and Mongolia, and mutual recognition.
However, neither the independence of Tibet or Mongolia were recognized by other powers which continued to recognize the sovereignty of the Republic of China over these areas. The interests of Western powers (particularly Russia and Britain) in these areas were guaranteed by treaties with the Qing dynasty which the Republic of China pledged to uphold and by recognizing the independence of Mongolia or Tibet, the Western powers would have invalidated those treaties. In addition, there was fear among the Western powers (again particularly Russia and Britain) that recognizing Tibetan or Mongolian independence would allow those areas to be controlled by other Western powers, a situation which all concerned believed to be worse than the situation in which those areas were nominally under the control of a weak China.
See also: History of Tibet