Since you are asking about the colonists, the time frame for the context of the answer is 1600 to 1876. Before 1600, there were European explorers coming to the Americas, but they were motivated by exploration—they were not looking to create a permanent settlement. The first encounters between Europeans and Native Americans were not always hostile encounters, as frequently depicted. Settlers were curious about Native Americans, and probably the indigenous population was equally curious about the settlers. In the early encounters, though, language and cultural differences were obstacles to understanding. These misunderstandings in part led to hostilities and reactive negative perceptions of Native Americans by the European settlers.
European settlers believed they were superior to the tribes they encountered. Understanding the history of Spanish explorers is useful in discovering how Europeans viewed the encounters with the Natives. The Spanish were unabashedly willing to use any means necessary to exploit the knowledge of Native Americans to further their goal of finding wealth. In a rush to "civilize," or force Native Americans to assimilate to European norms, the settlers enslaved tribes they believed were inferior. Europeans brought to America diseases which the Native American tribes had not encountered and had no immunity against. Disease literally decimated Native American tribal population.
French explorers took a much different approach. French explorers made an effort to integrate and understand the culture of the Native Americans they encountered. For the most part, French trappers had reasonably cordial relations with many of the tribes they encountered. The French were very successful in their efforts to maintain permanent settlements, with few open conflicts.
The British, early in the settlement process, had good relations with Native Americans. Though the track record of British encounters with Native Americans is mixed, for much of the early colonial period (since they were the predominant white colonists), there were some hostilities, but not to the extent one might imagine.
Background information is necessary to understand that the colonial attitude was a Euro-centric, white supremacist belief that European cultures were superior to those of the Native Americans. The Europeans believed they were superior to every culture, including Asian and African societies. It is not hard to see how this belief translated into a colonial culture that had no respect for Native Americans and their culture.
Intolerance never leads to good outcomes. The colonial prejudice to Native American culture continued forward into the next phase of American colonial expansion and growth. These periods were characterized by the major events of the American Revolution, independent self-government, and the idea of "manifest destiny." Increasingly, colonists justified the destruction of Native American culture as compliance with a divine call to settle all the continent, from coast to coast. Native American societies were viewed as an obstacle to growth, and the notion of a superior Euro-centric civilized culture was used to justify the removal of the "barrier" by any means possible. These colonial attitudes were consistent with European views of the time.