As another example: Henry Wirz was tried, convicted, and executed for running Camp Sumter (the POW camp near Andersonville, Georgia). As far as I know, nobody was ever tried for what happened at Elmira Prison. Elmira Prison had a 25% mortality rate, Camp Sumter had a mortality rate of 29%. Guess which one was run by the victors.
However merely being on the losing side isn't sufficient; you have to be on the conquered side. The US was by reasonable accounts on the losing side of the Vietnam War, but war crime trials were never held for the people that really deserved it because although the US lost, they were no conquered. Saddam was on the losing side of the Gulf War, but he did not see trial for his crimes until he was well and truly conquered many years later.
The Vietnam war was not a war of survival for the US, nor did it take place in US territory. Psychologically, it was certainly a blow, but in the chess game of geopolitical strategy, it was more on the level of losing a knight or bishop, certainly not losing a queen or the entire game.
However merely being on the losing side isn't sufficient; you have to be on the conquered side. The US was by reasonable accounts on the losing side of the Vietnam War, but war crime trials were never held for the people that really deserved it because although the US lost, they were no conquered. Saddam was on the losing side of the Gulf War, but he did not see trial for his crimes until he was well and truly conquered many years later.