I'm at a loss as to why anyone besides the Chinese would have seen their fall as a bad thing for the region or the world.
The United States did not want to see their recent adversaries to expand, especially since Vietnam maintained very close relations with the Soviet Union and leased a large naval base to the Soviets. Thailand was afraid that Vietnam's expansion would make them the logical next target.
The United States and most Western powers recognized Prince Norodom Sihanouk as the rightful Cambodian head of state. When the Vietnamese organized a new government friendly to them, Sihanouk protested to the United Nations.
So: While no one shed tears for the fall of Pol Pot, the only major actor that benefited from Vietnam's action was the Soviet Union.