Societies are complex and I don't know of one where such thinking was universally accepted within a whole community. However, during slavery, a genre of folktales actually appeared in Africa and in the Americas to explain the African enslavement and cultural subordination, what William Piersen (in Black Legacy) calls the 'God's gift to the races' genre. In these myths, Africans are said to be physically superior to whites, but too interested in riches and material things to successfully gain the 'gift' of knowledge, which allowed whites to dominate Africans. The pervasiveness of this myth suggests it contributed to a very negative self-image in the community. However, it should be pointed out, the slave community had many other tales wherein they claimed that whites were ultimately either equal to them or even inferior to them in some way.

It's unlikely: societies and in particular their spokespeople tend to have a vested interest in presenting themselves as "superior" to others. If that can't be done economically/technologically, then rhetoric of cultural/spiritual/ideological superiority tends to dominate. Check out the first treatise of Nietzsche's Genealogy of Morality for a prominent example.

Regarding your question more specifically, I can say that Social Darwinist thought generated a serious intellectual crisis in Japan in the late 19th Century. This was a period in which the new Meiji state adopted a very self-conscious process of modernization, importing wholesale Euroamerican technologies, political structures, scientific knowledges, etc. But according Julia A. Thomas in Reconfiguring Modernity, Social Darwinism – which was of course seen as a "science" at the time – proved incompatible with the state's nationalist ambitions: basically, according to the tenants of S.D., Japan's "backwardsness" meant that it could never catch up to the Powers; it lagged behind evolutionarily. This was unacceptable. So, after much hand-wringing, Japanese intellectuals basically redefined nature to rid it of its "universalistic and progressive implications," and instead found (which is to say, created) a vision of nature that squared with a ethnocentrist cultural practices.

So in short, Japanese thinkers recognized precisely that Social Darwinism would force them to regard themselves as inferior, and consequently did away with it in their sociopolitical frameworks.

This idea is still common among the Chinese liberals, I suppose Japan society might accept this idea late 19th century until nationalist control the country. If most people could accept they are not genius, nations also could accept they are not the best. Accept myself as "Lower People" compared to these genius doesn't mean they can discriminate me, but inspire me to work harder.

Social Darwinism is a progressive ideology at first and in Asia, it is anti-religions and anti-traditions. If old species with millions years of history could extinct, why not old political system with thousands years of history? Natural selection would doom countries without democracy and freedom, so we need to reform our country. BTW, Marxist also believe their version of social Darwinism.