If you don't see a sign saying "This is private property", your assumption is that it's public land? In the absence of a sign you had no way of figuring out that this wasn't a public, municipally owned parking lot?
So the issue is not that the lot was unmarked, but that somebody apparently vandalized the sign.Quoting FalconCane
The statutory requirements for signage are described in Florida Statutes, Sec. 715.07(5). Had the sign not been damaged would it have met the statutory requirements? What did the lot owner or towing company say when you reported to them that the sign was damaged, and that's why you didn't notice it? Did you take a picture? Has the sign since been repaired?

