This is a challenging question to answer because you are asking to explain an absence of something, rather than the presence of something. Thus, there aren't really any obvious sources to support a position. However, there are a few points I would argue.

The first is that both the Aztecs and the Incas were highland, agricultural, empires. Their primary powerbase rested on investing in irrigation and terracing, and controlling the farmers who worked the fields. In addition, their key trade routes were between highland and tropical regions, and were thus overland. Strategically speaking, the sea was a distant concern. The Maya (at least those in Yucatan), did live much closer to the sea, and paid it much more attention. They actually had quite a thriving costal trade. However, Maya city-states were much more politically fragmented than either the Aztec or Inca Empires, and thus lacked the organisation, wealth, or power, to really maintain a naval force. In addition, they had little need. Although sea raiders were common in the Caribbean, they don't seem to have affected the Maya much at all. This is true of all three peoples. None of them faced any real threat from the sea (before the Spanish arrived at least) and so had little incentive to push naval technology or to form a navy.

Having said all this, the Aztecs kind of did have a navy, but it was a green water navy, rather than a blue water navy. It mainly consisted of canoes, which were used to ferry troops for co-ordinated amphibious attacks around the lakes in the Valley of Mexico. Now, a canoe may not seem like the most impressive of ships, but they were well suited to the conditions. The water was too shallow for larger ships, and canoes were extremely easy to handle while also carrying heavy loads of both supplies and men. The Aztecs went a step further, even armouring their canoes so they could act as a defensive platform for archers. They used this to great effect during the Siege of Tenochtitlan, as Diaz reports, 'Our crossbowmen and musketeers fired continuously at them and their canoes, but hardly did them any damage, for they were well protected by wooden bulwarks.'

As far as I understand from the development of navies elsewhere in the world, they begin when nations have significant trading fleets that then encounter enemies that they need to fight on the water (usually over ocean resources and right of way to navigate one's ships through contested waters), whether those enemies are pirates or foreign nations. If all of your trade is over land, and all of your enemies are over land, the risk and the daunting level of material and engineering resources needed to develop a navy make it a pursuit not worth taking.

Extremely ancient navies before the development of naval artillery fought on the seas by either coming along side other ships to forcibly board them with warriors (what the Romans did, because they were best in such combat) or to ram enemy ships (what the Greeks and Carthaginians did). Hurling fire bombs onto enemy ships was also a tactic that was used, but before artillery (even ship-mounted catapults), the range at which this could be done was very limited, and the accuracy of primitive artillery on a ship out at sea was very poor. In the most primitive form, navies are just the sea transport branch of the army, for carrying an invading army to new lands. The Vikings were sea faring people, but their warfare entailed landing their ships and unloading warriors onto a beach. They did not engage in ship to ship combat as we understand naval warfare, perhaps because there weren't necessarily sea-faring enemies to do that with. Ramming enemy ships, which was a function of Greek naval vessels powered by teams of rowers, entailed very peculiar engineering. The prow of the Greek warship also had a huge bronze ramming cap to serve as the ram; bare wood by itself would not survive the impact of ramming another ship. The ship had to have a ram up front, and had to be structured such that a sharp impact to the ram would not rip the ship apart. Pre-artillery navies are not a sure-thing in military development unless necessity forced the kind of thinking that led to this kind of result.

Another factor that should be considered is that the Aztecs, Incas, and Mayans were stone aged peoples whose work with metals seemed to be limited to gold and perhaps copper. Real naval development seems to only arise in bronze-age or later cultures. Bronze can be used to manufacture nails, saws, and chains, and perhaps anchors. Without the invention of the nail, the size of the wooden ship that you can build is extremely limited unless you used extremely sophisticated joinery along with tar for sealing the joints. However, without the invention of the saw (which cannot realistically be made of stone) a culture's ability to work with wood to make ships is also extremely limited, and sophisticated no-nail joinery (such as seen in Japanese carpentry) would be impossible. Perhaps a well made metal ax may be able to hew wood well enough to make boards and planks and other ship-building materials, but stone axes are not likely to have been able to be used for effective shipbuilding.