When Trotsky states that there is no doubt that the goals of the Russian Revolution will not be realized until there is a worldwide embrace of Socialism, it prompts concern around the world. The implications of the Russian Revolution all over the world were fairly profound. On one level, the Allied powers were concerned because a traditional "top- down" government had been disposed of with such force and such clear repudiation that it made other nations that were so "top- down" worried. A Russian population, largely composed of illiterate peasants and poor people, took up against their government and disposed of them, even going as far as executing them and their family. That was fairly startling for the rest of the world, especially the Allied Powers. For nations in Europe, all of which were governments where a ruling elite made decisions for the rest of the people, the events in Russia were startling.
From an economic point of view, the idea of a Socialist government that was purportedly professing their loyalty to Karl Marx and Vladimir Lenin caused significant concern to the Allied Powers. The Allied governments were very quick to be worried as they were mostly capitalist governments, whose existential threat of socialism was the essence of worry. The structure in which capitalism would be challenged by socialism was to be played out in nations already industrialized, such as France or England. For this paradigm to be developed in a non- industrialized nation like Russia was highly worrisome, as it helped to bring out that Allied nations could be "next."
Finally, I think that the Allied powers were worried by the Russian Revolution on a metaphysical level because it signified a seismic change. When Virginia Woolf writes, "All human relations have shifted," this dynamic is most evident in the Russian Revolution. For generations, the Russian tsar had been seen as the function and embodiment of power in the nation. The absence of Russian royalty as well as the emergence of terms such as "Provisional Governments" or "Bolsheviks," helped to bring about a significant change in how the Allied nations could view Russia, and in the process, themselves. This fundamental "shift" in human relations and political relations with the largest nation in Europe helped to bring out some level of worry and concern in the Allied nations.