The traditional response to this is adversely because the major colonial empires had access to eastern markets and did not have to go through the Ottoman middlemen. Furthermore, the productivity of the sugar plantations in the Caribbean and Brazil far outstripped the productivity of Venetian plantations on Crete, which had become a major source of income.
While I think that the ability to avoid a middle man led to a gradual decline in Mediterranean commercer is largely true and it does ignore some other issues. While the Ottoman Empire did seek to gain money from tariffs, they were hardly debilitating and we find numerous examples of French, and later British, merchants operating in the major ports of the Ottoman Empire. I think one of the biggest problems facing the Italian city-states was their inability to compete with the centralized monarchies north of the alps. As early as the 1350's we see the Crown of Aragon assisting Venice against Genoa. Although Genoa was able to hold of this threat and the war fought between 1350 and 1355 was essentially a stalemate, the introduction of an increasingly centralized kingdom in the western Mediterranean with an ever growing population and expanding economy meant that little Genoa would eventually be outstripped. By the end of the 14th century the French king was meddling in Genoese politics and the city would eventually become a pawn. Although Genoa experienced something of a Renaissance under Andrea Doria and the oligarchic republic he founded, the city essentially operated as a naval representative of Spain and helped to run the finances of the Spanish crown.
Venice endured the transition out of the Middle Ages more successfully than her old rival. I think the stability of la serenissima had a lot to do with this fact. The French king was invited into Genoese politics in the 1390's because the citizenry of the city was unable to solve the endemic strife within the republic. Venice, with her impressively stable (if insanely complex) governmental structure allowed her to survive. Additionally, the more unified commercial policy, I think, allowed Venice to present a more unified economic face to the world. Furthermore, Venice was able to sell salt from her lagoons, a valuable asset that made her money until Napoleon dissolved the republic. Finally, Venice's colonial holdings on the islands of the Aegean remained out of reach of the Ottoman Empire for some time. Genoa's major colonial holding was an advantageous holding in Constantinople (although they remained after 1453, it last it's prestige) and the Crimea, which became less lucrative after the Ottomans asserted control over the Bosphorus.
Pisa was already a nothing by the early modern period and Florence is a different issue, but like the other city-states, her power was outstripped by the centralized monarchies north of the Alps.
Adding to /u/Enrico_Dandolo/ , Spain's rise in the Americas coincided with growing financial dependence on its constituent kingdom of Castile. It provided a reliable tax base which is then used by the rulers to gain credit, which is then used to raise a navy for the trans-Atlantic trade, a navy for Mediterranean patrol, and multiple armies all around Europe (and the world).
In the early 1500s, Spain's naval strength was weak. So Charles V and Philip II relied on Genoa to provide a navy for the Mediterranean and beyond, in addition to Genoese bankers providing funding for the expeditions.
The growing importance of Castile's economic engine meant that the mesta, a medieval guild of sheep herders in Castile, rose in importance, which displaced farms through a mix of political and religious conflict. In turn, this increased Castile's reliance on imported grain from the Majorca and Sicily. This period also saw Naples fall under control of Aragon.