It's important to start from the key point that post-modernism is based on conceptual relativism. That is, from the doctrine that concepts are not defined individually but within a language, that is, in relation to each other. That means that they have the needs and interests - the values - of the language users who construct them embedded in them.
So, for example, "civilization" meant Western or European civilization, including its values and priorities. So other civilizations could not be recognized and respected as such. Conquest and colonization could be justified as in the interest of those being conquered and colonized. The other interests at play (primarily economic) could be hidden or justified. The demand for equality and freedom, within such a system, could be seen as irrational and dismissed or ignored.
Post-modernists also held that people's abilities and values were largely formed by the society in which they grew up, including the ideas and language that they learned. The result was that many of them were unable to articulate their own needs and desires.
Post-modernism was primarily a critical movement and did not need to articulate alternatives, beyond the demand for recognition and equality. Arguably, it would have been inappropriate for anyone but those being emancipated to work out what happened next. But the critique of reason did not necessarily mean it had to be abandoned or replaced; all that was required was/is to revise it.
I'm not sure why you cite Sartre in this context. He was certainly not a post-modernist. His existentialism treated the individual subject as primary in contradiction with the post-modernists who saw the individual as socially determined.