The Most Serene Republic of Venice, while one of the greatest Mediterranean trading Empires in all of history, also possesses a very checkered past, riddled with treachery and deceit and driven by an insatiable desire for political power and economic domination. It is because of this that, like Byzantium, the historical name of Venice comes with a certain element of notoriety within historical circles.

Perhaps the greatest reason for their notoriety is because of their role in the brutal Sack of Constantinople in AD 1204, which broke the heart and soul of the Byzantine Empire, arguably the most advanced and well-developed state in all of Europe at the time. Furthermore, the fact that the Venetian Crusaders sacked a holy Christian city (one of the holiest, in fact - the "City of Constantine", one of the last remaining vestiges of old Rome, and the greatest city in Europe for almost 900 years), when their goal was to "liberate" Jerusalem from the Muslims, makes the act even more despicable. And finally, consider that the Venetians (once allies of the Byzantines, and a group of people who began their rise to prominence as a Byzantine colony) had everything to gain economically by removing the Byzantine customs and excise taxes from the Venetian economic equation (even when special concessions were made for Venetian traders under Alexios I Komnenos and his successors). They even had the courtesy to continue taking lands from the Byzantines (such as Crete and Corfu), even after they had dealt the Empire its crippling blow. Keeping in mind all these things, it makes it pretty hard to view the Venetian Maritime Republic as righteously guided and respectable state.

However, despite the derisive tone I have set forth, one must also consider that the Venetians who sacked Constantinople were seeking revenge for several thousand of their merchants who were slaughtered when the xenophobic tyrant Andronikos I stormed the Byzantine capital and usurped the throne from the rightful heir of Manuel I Komnenos, Alexios II, in 1183. They also sought to take advantage of the weak and incompetent Emperors who followed Andronikos, the Angeloi, who neglected to rule the Byzantines in an effective way and set up the Empire for disaster.

I do feel, however, that despite these events, the Venetian solution was contemptibly extreme and is likely a partial origin for the phrase you've described. In a way, this Venetian treachery and greed was made to be a convenient scapegoat for Europeans (especially Greeks, though), giving rise to the phrase "those damned Venetians".