I was recently at the Museum of Science Boston's exhibit on the Mayan culture, and while it was a very interesting exhibit full of new knowledge, for me the artifacts just didn't compare to ones I've seen from Ancient Greece or the Roman Republic, or even from ancient China and India. Why is this?
This is a common misconception, in truth mesoamerican and south american cultures were very advanced, just in ways that were different than what is typically thought of as "advanced". Early American civilizations had very complex construction and architecture techniques as well as metallurgy and textiles.
When people say that "they weren't that advanced" people are usually referring to the fact that the Incas didn't use wheels. Long story short; They did. But American cultures didn't use extensively for a couple of reasons, namely they didn't have any draft animals. Cattle and horses simply didn't exist in the american continents at the time. Llamas aren't very strong, and the American Bison was never tamed. This, in combination with the many steep, rocky, mountainous regions of the american continents meant that the wooden cart wheels of the time simply weren't useful to them on a large scale.
Another reason they tend to be thought of as less advanced is that the american cultures tended to favor natural defenses instead of the artificial method of castle building. See Machu Picchu and the Cliffdwellers. Those, and many construction sites like them had very advanced construction and carving techniques employed throughout them.
There was also Tenochtitlan the capital city of the Aztecs that was built in the middle of a lake using a combination of natural and artificial islands, complete with huge drawbridges that could be raised in case of an attack. This wasn't just one fortress either, the entire city was built like this. And in some places there was even running water thanks to two large aqueducts flowing into the city.
And then we come to Teotihuacan a massive city that existed centuries before the aztecs built Tenochtitlan. It is thought to have housed at least 125,000 people during its height making it the 6th largest city in the world at the time. These were the people the Aztecs worshipped as gods!
There are a couple of other reasons why they aren't thought of as "advanced" including their highly fragmentized cultures, their lack of large scale warfare (there are exceptions, but most ancient american conflicts were relatively small and over pretty quickly compared to the grand battles of european military history), and the difficulty of obtaining certain materials made certain tasks more difficult for the people of the american continents.
TL;DR The many American cultures were advanced, in some cases just as much or moreso than their european counterparts. But due to differing circumstances and environments, they never developed, or never needed to develop those technologies in the first place.