To some extent this answer requires speculation, since as far as I'm aware there aren't explicit texts or recorded interactions that explain why the Aztecs never attempted to conquer the Caribbean islands. I'd also like to say that Aztec expansion was not simply a quest for more sacrificial victims; the empire expanded to subjugate rivals, increase tax/tribute revenue, and many other reasons that are common to imperial states throughout time and space. However, your question is still an interesting one. The Aztecs were certainly aware of the Caribbean, since much of their empire bordered that sea (this is true for all the variously disagreeing maps we have of the empire). It is not clear how much they knew about the Caribbean islands - for example, we have no evidence they were aware of Cuba - but that raises questions about why they may not have even initially expanded into or explored the Caribbean Sea. I'll propose three potential reasons why the Aztecs never chose to go out and expand into the Caribbean: means, cultural difference, and perhaps most importantly, simple lack of motivation.

The first reason I'd suggest is because the Aztec Empire was at its core a terrestrial state that specialized in land-based warfare and control. Of course the Aztec Empire made use of aquatic trade routes and had a significant brown-water navy^(1), which played an important role in the battles against Spanish conquistadors. But the Empire's conquests invariably subjugated places that its devastating land armies could reach. The Triple Alliance has been called "arguably the most transportationally constrained empire in world history... In their imperial expansion, the Aztecs expanded over hundreds of miles from their capital without draft animals, wheeled vehicles, sails, or the aid of any other form of mechanical transport" (Hassig 2015)^(2). For our discussion here, the most important part of that quote is that the Aztec did not make use of sails that could ease potential conquest and control over the Caribbean. It's important to remember that most of the Caribbean is far from Aztec territorial lands; the distance from Aztec lands on the Caribbean coast to Cuba's western tip is about 1,200km, is farther than the distance between the Aztec Empire's northern and southern ends. The Empire's focus on a terrestrial military and lack of options for controlling land overseas would have made exploring, conquering, and holding the Caribbean extremely difficult

Second, let's talk about cultural difference. The Aztec Empire was situated in continental Mesoamerica, an ancient center of civilization that had developed hundreds of forms of urban societies even before the Aztec appeared. The incredibly variety displayed by Mesoamerican societies does not detract from the reality that the region had intricately shared cultural and historical characteristics. Areas from Central Mexico were in contact^(3) with Mayan states, common religious features^(4) existed across the area, and various other factors linked Mesoamerica into a cultural atmosphere. The Aztec Empire certainly conquered many different groups in Mesoamerica, but it never left this greater sphere of shared culture and history. By the time of the Aztecs, it seems like^(5) most of^(6) the Caribbean was inhabited by people descended from settlers traveling outwards from northern South America. Whatever the exact case, Caribbean peoples had their own sphere of shared culture which was clearly different from that of Mesoamerican societies. This may have been another pressure that decreased the likelihood of Aztec expansion and exploration in this direction.

In some ways, the final part of my answer brings together the two previous paragraphs. If the means were difficult and doing so would mean a significant jump in culture, why would the Aztec focus on the Caribbean to the detriment of their goals in mainland Mexico? The Aztec had by no means conquered all of their urbanized neighbors. For a few examples, Maya kingdoms in the south lay virtually untouched, several antagonistic independent states existed as enclaves within^(7) Aztec borders, and the Aztecs' northern border was dominated by the existentially threatening Tarascan^(8) state. Regions like these were alternatingly more important or more feasible targets for Aztec imperial ambitions. They had a shared culture, were located nearby and on land, and were part of a constantly competing Mesoamerican community that the Aztecs had seen remarkable success against.

So in the end, my answer is: pressures made for easier targets for exploration and conquest than the Caribbean. Your question also asked about whether or not the Aztecs had the ships necessary to reach the Caribbean. We don't have much evidence that they did reach the Caribbean by boat, but we know that many people (that is, the settlers who made it there) did, and that other Mesoamerican societies like the Maya had extensive maritime networks^(9). So my answer leaned more towards addressing why the Aztecs did not even have the pressures to focus on technologies which would have allowed for Caribbean imperialism.

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Sources

^(1)Nahua Account of the Noche Triste, Florentine Codex (excerpt). (2017). In J. M. Francis, & T. M. Leonard (Eds.), Latin American history and culture: Encyclopedia of pre-colonial Latin America: (prehistory to 1550s).

^(2)Hassig R. (2016). "Aztec Logistics and the Unanticipated Consequences of Empire." In: VanDerwarker A., Wilson G. (eds) The Archaeology of Food and Warfare. Springer, Cham.

^(3)Jordan, K. (2016). From Tula to Chichen Itza: Implications of the Epiclassic Sculpture of Tula for the Nature and Timing of Tula-Chichen Contact. Latin American Antiquity, 27(4), 462-478.

^(4)Heyden, Doris, et al. "Mesoamerican Religions: Mythic Themes." Encyclopedia of Religion, edited by Lindsay Jones, 2nd ed., vol. 9, Macmillan Reference USA, 2005, pp. 5933-5939.

^(5)Siegel, E. et al. (2015). "Paleoenvironmental evidence for first human colonization of the eastern Caribbean." Quaternary Science Reviews, 129, 275-295.

^(6)Lalueza‐Fox, C., Gilbert, M., Martínez‐Fuentes, A., Calafell, F. and Bertranpetit, J. (2003), Mitochondrial DNA from pre‐Columbian Ciboneys from Cuba and the prehistoric colonization of the Caribbean. Am. J. Phys. Anthropol., 121, 97-108.

^(7)Fargher, L., Blanton, R., & Espinoza, V. (2010). Egalitarian Ideology and Political Power in Prehispanic Central Mexico: The Case of Tlaxcallan. Latin American Antiquity, 21(3), 227-251. Retrieved December 5, 2020

^(8)Stawski, C. J. (2012). Settlement systems, landscapes and the rise of the tarascan empire: A settlement analysis in the lake pátzcuaro basin, michoacán, mexico (Order No. 3548623).

^(9)Jaijel, R. et al. (2018). "Coastal reconstruction of Vista Alegre, an ancient maritime Maya settlement." Palaeogeography, Palaeoclimatology, Palaeoecology, 497, 25-36.

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edited because I clicked comment before I finished!

edit 2: to clarify sources