Keep in mind that you don't have to go for objectively justified—if there can be such a thing for wiping out a people—since people can be irrational about their emotions or feel them based on incorrect facts. Particularly if it's people of a state instead of an individual, thus involving propaganda and such, although it's not clear which you're after.
And just because it's something horrifying doesn't mean history must be obsessed with that legacy. Winners write the history books and everything. It could be framed as a war that they won, or an extermination of evil (like those fantasy plots where the enemy is a race of orcs/demons/vampires/whatever), or just swept under the rug so that twenty years later children aren't really learning about it as anything more than a footnote unless they do their research or hear from their parents and grandparents. Particularly if there isn't the rest of the world forcing them to remember it, there might be no reason to write it into history textbooks as anything but exactly how they want it to be remembered. It can also be remembered as something shameful (but it's all in the past, done by less advanced people, and restitution is conveniently both unnecessary and impossible), and if they learn it in an academic setting, most kids will forget about it the week after their last exams anyway. The lesson doesn't have to be that you should murder those who wrong you, any more than what people learn today. And, well, you might consider that idea more or less frightening, but people moving on with their lives is the most obvious result.
More immediately, I think people would be more concerned about how it directly affected them
. Maybe families were on rations because of the "war effort" and the children carry that memory closer to their hearts than the deaths of however many people. Maybe someone's business thrived because they offered the closest non-rationed substitute to a commodity people wanted. Maybe the soldiers too felt they were justified in their actions and were in it for glory or because they really thought it was the right thing to do. Maybe someone had to cut ties with their targeted friend out of fear and then never heard from said friend again. Maybe people involved with mass execution facilities didn't personally see much beyond the button they had to press, and it was just a job and they did it and went home to their loving families and had the money to put food on their tables. Maybe technological advances happened more quickly and that has a greater effect on society than the genocide itself.
You'd have to worldbuild and give more details on the scenario—politics (worldwide and national), attitudes of the people involved, attitudes of the people not directly involved, culture, the reason for the genocide in the first place, how intrusive it is on people's daily lives, et cetera—if you're looking for anything more directly helpful to any story you want to write or whatever, though.
You will not go to space today.