Well, Austria wanted to controll Italy, not to conquer it. That is a slight, but important difference. The only land ruled by the Habsburgs - until 1708 - was the Duchy of Milan, and even that was controlled by the Spanish line, which wasn't always so much attached to the Austrian line than many may think (the Reichsvikar/Imperial vicar of Italy was still Savoy, even when Felipe II insisted, that he should gain this title as a duke of Milan; Ferdinand denied). Austria thought much more in the terms of an HRE than as a land power. Mantua was gained because the Gonzaga died out (fief without holder). Milan was inherited/gained in the War of the Spanish Succession (like Naples, which later was lost). Tuscany was a recompensation for Stefan of Lotharingia, after the Medici died out.
Regarding Venice: clearly, the League of Cambrai was a huge blow. But the League of Cognac didn't see much engagement on the venetian side. The War of Gradisca in the 17th century had much more impact on the relation. On the other side, Venice was allied with Austria in 1495 against France, and in several Wars against the Ottomans (not only the famous one after the siege of Vienna, Austria did also support Venice indirectly in the long War of Candia). The relation between both nations were as ambivalent as the relation between Venice and the Ottomans. Aside from Riva, Rovereto, and some holdings on the coast of Friuli - all territories too tiny to show them on a map of EUIV - Austria didn't conquer anything in the north east of the peninsular. After the mid-17th century, Austria was much more interested in a naval power which could keep the Ottomans in check. After the middle of the 18th century, when Venice had lost its leading power in the Eastern Mediterranean, Austria didn't intervene either. It seems, that the role of Venice as a stabilizing, regional power was also in the interest of Austria.