This is adapted from an earlier answer of mine

I have once tried to track down this number, and found the best short discussion of it's origin and veracity in Frederic Lane (he is authority for Venetian ships and shipbuilding) and appendix II of his book Venetian Ships and Shipbuilders of the Renaissance (link to Google Book fragment). There is also more discussion and description in Lane's article Venetian Shipping During the Commercial Revolution from which I took the quotes.

The number of 3,300 is taken from oration of Doge Mocenigo who gives the number of 3,300 (or 3,345 actually) as a rough count of all ships, small and big, owned by Venetians, not specifically state owned "navy". Think of it more as a total count of all ships rather then purely military vessels.

Mocenigo divides the ships in three categories:

• 45 galleys manned by 11,000 men
• 300 navi ships manned by 8,000 men
• 3000 small ships manned by 17,000 men

Lane tries to verify such numbers and finds them plausible (if maybe slightly large) For example, crew count for galleys or "galere" is given by Mocenigo is 244 per galley, while Venetian senate orders state they should have 212 men per galley. The small discrepancy shouldn't bother us. Lane also counts that every year Venice sent out at least 16 galleys on commercial voyages ("Romania and Tana -3 , Alexandria -3, Beirut - 4, Flanders and England - 4, Aigues Mortes - 2") and also had at least 10 war galleys each year on patrol duties, so total of 26 per year minimum. Add a few private galleys and the fact that Venice had extra galleys for time of war and the number of 45 isn't out of the ballpark.

Lane describes the galleys as:

These great galleys or merchant galleys were not particularly large vessels compared to many of the Venetian round ships of the time. They carried between 140 and 250 deadweight tons of cargo below deck. Though smaller they were considered safer than the round ships because in addition to the sails on which they relied during most of the voyage the galleys had oars to use in entering and leaving ports. Moreover they were warships with crews of over 200 men armed as the Signoria might direct and commanded by a noble whom it selected.

For the "navi" ships Lane concludes those are so called "round ships" (the closest we would call them is carrack) and all are above 100 tons (400 Venetian botte), and them being crewed by 20-30 men is very ordinary. Their number of 300 is really hard to verify though, but given that 100 ton size isn't that large, and those ships were mostly utilized in trade in Adriatic and between closer Venetian possessions, it is a possiblity.

Lane describes them:

But the bulk of the Venetian merchant marine was composed of round ships. In the proverbial golden age of Venice, roughly from I420 to I450, she had 300 such ships of 100 deadweight tons or more. Most of these 300 were probably used for fishing or for carrying about the Adriatic such humble cargoes as grain, oil, wood, and stone, and did not figure as long distance carriers on the great routes of interregional trade. But it may be estimated that at least thirty to thirty-five of them were ships of 240 tons or more and were habitually used on voyages beyond the Adriatic, mainly on the longest well-established voyages such as those to England, Syria, and the Crimea. They were the great merchantmen of their day, distinct in rigging and in structure from the coasting vessels.

In the end, what is termed "navigle" are the smallest ships of under 100 tons and crewed by 5-6 men avarage, which is entirely possible. Those were the numerous small fishing vessels, and small ships utilized by local populations to move around and do various everyday stuff, so it shouldn't really be strange. I think nobody really ever counted them, but putting them in the thousands wouldn't be strange. However those ships would never be a part of a war fleet as such (except as auxiliary vessels)