The most important reason is that from the beginning of the European colonial period until unification Italy was made up of small states that were under foreign domination. Just as the age of discovery was getting started Italy was invaded by France, Spain and other countries in the Italian wars (1494 - 1559). These ended with Spain dominating Italy from 1559 - 1713, and subsequently Austria dominating it 1713 - 1796, ending with Napoleon's occupation. So during this period Italy was more like a colony of outside powers itself than an independent power able to establish its own colonies. During the 19th century prior to the date of 1866 that you give, Italian states were too preoccupied with overthrowing the Austrian domination that had been restored with the congress of Vienna 1815 and with the unification struggle to give a thought to foreign colonies.

It's an interesting question whether Italian states would have established colonies in Africa during the period that other European states were in the absence of foreign domination. I can't give an answer but there are several factors that would mitigate against it. Some relevant factors are the following:

• Before the age of discovery, Italy (Venice specifically) was the centre of European trade with Asia, via the Ottoman or Egyptian Mamluk empires.
• Portugal and Spain, motivated by desire to circumvent these trade routes, and by an anti-Muslim crusading spirit, find alternative trade routes to Asia, and America, dividing the new opportunities up between them in the Pope approved treaties of Tordesillas and Zaragoza. Therefore Italian states lose out here, even in the absence of the subsequent Spanish occupation, as their trade monopoly with Asia is broken. Venice actually supported Mamluk egypt against Portugal once Portugal started capturing Indian Ocean trade for itself.
• From the late 16th century into the 17th century, Protestant powers reject the Catholic Spanish and Portuguese monopoly on the new discoveries (see Dutch Hugo Grotius' 'free seas' proposition), resulting in competition for the Portuguese in Africa and Asia, with many colonies being taken over by the Dutch. Italy, being Catholic, may not have been able to reject the Portuguese African monopoly so easily from a legal perspective.

So Italian states had weaker motivations than other European countries to establish colonies, even in the absence of foreign domination, prior to the national-prestige driven colonialisation of Africa in the late 19th century.