This is actually a very interesting question, and two years ago I heard renown American historian Peter Wood talk on in this exact question. In many ways the question is completely valid considering some Native American cultures (including the Maya, Aztec, Inca, and the mound building Mississippians) built large cities that rivaled contemporary European metropolitan development. Furthermore, evidence indicates that many Native American cultures (from the Iroquois in the American Northeast to the Incas in the Andes) were fully invested in intercontinental trade that brought goods from Gulf of Mexico as far north as modern Seattle. Considering that Native American cultures built large metropolitan cities and conducted transcontinental trade, it is entirely fair to ask why their ship building did not mirror Europeans.

However, I would also stress that there is ample evidence to demonstrate that Native Americans did indeed build large "ships" to transport goods and people. Wood's research was on the thriving metropolis of Cahokia just outside modern St. Louis. Evidence suggests that the ancient city was once situated along the banks of the Mississippi River and archeological work has uncovered large canoes that indigenous peoples used to conducted trade to and from the city via the Mississippi. In addition, peoples of the Caribbean and Northeast also built large canoes capable of traveling between islands or along the eastern seaboard.

This is also not to suggest that these ships in any ways resembled European frigates able of conducting transatlantic, or eventually circumnavigational, voyages. I would suggest here that the reason European and Native American shipbuilding differed was in looking at their objectives. While Native American people certainly conducted trade with other peoples across the continents, it appears there was little trade of large scale agricultural goods. Furthermore, following the closure of the Middle East to European Christians, many navigators began to design ships capable of much longer voyages to reach the Far East; in contrast, though goods traversed North America, there is little evidence that groups of indigenous people ever completed such long journeys. Finally, it is also worth considering the process of colonization. Beginning with the Spanish but cresting during the 17th and 18th century, Europeans moved across the Atlantic in large numbers and also began forcibly transporting millions of African slaves. While Native Americans had versions of slavery (even before European contact) and also conducted large scale wars against other peoples, they did not participate in large scale colonization processes that would have required the same type of shipbuilding techniques.

TL:DR: Native Americans did build large ships; however, these ships served very different purposes and therefore do not resemble their European counterparts.

Sources:

Robbie F Ethridge. Mapping the Mississippian Shatter Zone.

Daniel K. Richter. Trade, Land, Power: The Struggle for Eastern North America.