It is difficult to conceive how under any circumstances one culture can superimpose itself on another culture and consider itself justified in doing so. The Spanish destruction of the Inca and Aztec cultures is no exception. They are rather classic examples of exploitation and Social Darwinism at their very worst.
The Spanish had only one aim: to exploit and carry away all the gold and wealth they could from both Indian societies. Spain at the time was the poorest country in Europe, and it was widely believed that a large influx of gold would solve its economic dilemma. Although they made a half hearted attempt to disguise their invasion as an effort to "Christianize" the Indians, this was nowhere near their true goal. Hernan Cortez told Montezuma, the Aztec emperor
We Spanish have a disease of the heart which only gold can cure.
Many of Cortez's men drowned attempting to escape from the Aztec capital when they fell through the suspension bridge connecting the city to the lake shore because they had weighted themselves down with gold and jewelry in an attempt to steal it. Francisco Pizzaro likewise kidnapped the Inca emperor, Atahualpa, and promised to release him when his people filled a room with gold and silver for ransom. Not surprisingly, when the ransom was paid, Pizzaro went back on his word and had Atahualpa executed on charges that were obviously trumped up. As far as "Christianizing" the Indians, all that the Spanish accomplished was to destroy many artifacts which has cost much of those cultures to be lost to history forever.
The Aztecs were not "evil;" although they tended to be harsh to the people under their rule. (Not that the same cannot be said of the Spanish!) They believed that the sun, their chief god and the source of all life, survived only as long as it was fed a constant diet of human hearts. Repulsive as this is to western minds, to the Aztec, it was an abject necessity if the world was to survive. The Inca did not practice human sacrifice at all, and in fact enjoyed excellent relations with the people whom they had subjugated.
The Spanish exploitation of the Inca and Aztec was no more than a rather graphic instance of presumed European superiority superimposing itself on another society. Europeans in more than one instance claimed superiority and mercilessly exploited others claiming their goal was to "civilize" (translate that as "Christianize") them. To claim "justification" for such actions is tantamount to one killing ones parents and begging for mercy because one is now an orphan. Such a position defies belief.
The answer to this depends almost completely on your attitudes as to when, if ever, cultural imperialism is warranted. You can make a case that it was warranted in the case of the Aztecs, but less so in the case of the Incas.
The reasoning here would be that the Aztec civilization was simply evil where the Inca one was not. The Aztecs, with their emphasis on human sacrifice, do not seem to us like a very good civilization. You could argue that practicing cultural imperialism against them was a good thing, like stopping the Holocaust. You cannot make the same argument with regard to the Inca because they did not do human sacrifice on anywhere near the scale of the Aztecs. (Of course, the ones they did sacrifice were children, so you could argue that cultural imperialism was acceptable there as well.)
Of course, the system the Spanish brought in was pretty exploitative on its own. They didn't sacrifice the natives, but they did use them for their own benefit. So it's easy to argue that the Spanish regime was not morally better than the native ones were. If you feel that way, or if you feel that cultural imperialism is never justified, then the preceding argument holds no weight.