In short, Ottomans did not invade Italian Peninsula because they weren't able to, not for the lack of plans or attempts. On the contrary, between the fall of Constantinople and the Karlovitz treaty in 1699, Ottomans made continuous attempts to conquer this particular region.

The Italian states (Genoa, Venice, Milan, Naples) were not big in territorial sense, but they were extremely rich for their limited area and population and were able to maintain large armies, whether hirining the best mercenaries the era had to offer or maintaining well-equipped militia. Furthermore, in the late 15th and for the large part of 16th century, Venice and Genoa boasted the best navy in the Mediterranean and one of the best navies in Europe, making the invasion from the sea or even achieving naval dominance a very hard task for Ottomans or any other contender. The Italian states were often at odds politically and economically, but the conflict with Ottomans shown that they will be able to ally in face of mutual danger and they had a very powerful ally in Habsburgs who secured the territories bordering with Ottoman Empire.

At the time when Ottomans started to expand westwards, Habsburg lands included modern Spain, Sardinia, Kingdom of Naples (southern half of Italian Peninsula), Sicily, Duchy of Milan, large part was it now Austria and Western Hungary, as well as Bohemia and Silesia. Furthermore, Habsburgs under Charles V had amiable relations with Republic of Genoa and Portugal, further strenghtening their grasp on the Mediterranean. This mean that to capture Italian Peninsula, Ottomans had to face combined forces of Habsburgs and Venetians who. It is worth noting that the relations between these two powers were strained, especially after Venice's refusal to assist besieged Malta in 1565 was is considered to be one of the major factors that contributed to the Ottoman capture of Cyprus, but the Papal mediation allowed them to cooperate against the common threat.

Additionally, there were the Knights of St. John holding the strategic keypoints that were islands of Malta and Gozo as well as the mainland base in Tripoli (now capital of Libya). Despite relatively small numbers, they have proven more than a match for the Ottoman forces who tried to dislodge them from their former holdings on Rhodes and failed to do so in 1480. The next siege in 1522 was successful for Ottomans, but even then they lost almost a third of their forces despite outnumbering the defenders by at least 30 to 1. After dislodging the power of the knights, Ottomans under Suleyman I and Selim II were continuing their efforts to secure dominance in the Mediterranean, unsuccessfully attempting to capture Malta in 1565 and conquering Cyprus in 1570, what directly led to a confrontation with the Western fleet in the battle of Lepanto in 1571 that, although ended with crushing defeat of the Ottoman navy, the latter was able to rebuild in a short time.

Summing up the above, the westwards expansion of the Ottoman Empire was resisted by very powerful opponents and thus the goal of conquering the Italian Peninsula was very difficult to achieve. It didn't deter the Ottomans though, as after conquest of Shkodra and subjugation of Albania in 1478, Mehmed II managed to capture Otranto in 1480 and indeed planned to attack Rome, but this plan was thwarted by Sultan's untimely death next year. After the successful siege of Rhodes, they started to expand. In 1525 Ottomans moved northwest, invading Hungary, defeating the Bohemian-Hungarian forces in the Battle of Mohacs in 1526. Death of Louis II, king of Bohemia and Hungary, who fell in battle meant that, pursuant to the agreement made during Congress of Vienna of 1515, Habsburgs gained control over the Louis' lands. After initial victory, Suleiman had to focus his attention elsewhere, allowing his opponents to launch a successful counteroffensive, although the victory was short-lived as in 1529 Ottomans recaptured the lands and were able to invade Austrian lands and besiege Vienna. It is worth noting that this campaign was initially aimed precisely at the capture of Italian States with the assist of France that would attack the Habsburgs from the West. This plan, however never fell through as both Ottoman Empire and France we interested in conquering Italian states and thus their goals were contradictory. Later, Ottomans attacked the Venice territory both in the Aegean sea and in the east coast of Adriatic along with the expansion by land into Dalmatia in the years 1536-1540, ending with the capture of Aegean islands and parts of Dalmatian region belonging to Kingdom of Hungary so that the Venetian lands were bordering now with Ottoman Empire, exposing them to a direct attack by land.

The Ottomans later made several more attempts of capturing Habsburg lands, most notably in 1593, when they were defeated at Sisak, 1663 when they expanded their holdings in Hungary and in 1683 when they managed to besiege Vienna again. The last campaign proved disastrous, as the defeats at Vienna and Zenta in 1693 directly led to the treaty of Karlovitz, where Ottoman Empire ceded most of their lands lands conquered in 16th and 17th century: Hungary and Transylvania to the Habsburgs, Podolia and Right Bank Ukraine to Poland, Dalmatia and Peloponesus to Venetia and Azov to Russia. This event marked the end of the successful expansion of Ottoman Empire into continental Europe bar few localised exceptions. As one can see, despite conquering a majority of Hungarian territory, Ottomans were unable to break further into the Habsburg territory, at least not deep enough to threaten the Italian Peninsula from the land.