Plenty of Victorian novels address the reader: Dickens did it all the time. That doesn't make him a postmodernist.
Briefly, read almost any novel written before the twentieth century, and you have a sense that the author is saying: here is the world and it is possible to have a full and complete picture of it. Modernism didn't take hold until the early twentieth century. Anything written in the earlier style before then is pre-modernist, anything later is anti-modernist. (Unless it's postmodern pastiche, more later.)
Early Modernist writers include Henry James and Joseph Conrad. What they seem to be saying is: here is the world and it MAY be possible to see it whole, but we can only see a partial or incomplete picture of it. Hence ambiguity and possibly unreliable narrators (cf. James's The Turn of the Screw), uncertainty and insecurity, non-linearity (Conrad was one of the earliest exponents of flashbacks). This tied in with movements in other arts, such as music and a breakdown of previous certainties, a process accelerated by the First World War. Also tied in with this was an interest in reproducing the flow (or "stream") of human consciousness - more an emphasis less on what happens than what is going through the protagonist's head as it happens. See novels by James Joyce, Virginia Woolf, some William Faulkner, etc. Many of these devices and themes have been so absorbed into western culture that we don't notice them any more. Most fiction nowadays, certainly most literary fiction, is modernist.
Postmodernism goes a step further, in denying that there is some objective truth or world out there and our ability to contain it. Often characterised by irony, deliberate pastiche of writing styles (usually to show up its assumptions and hidden values and to emphasise the artificiality of literary forms), emphasis on life's absurdity, black comedy and so on. Hence you get things like extreme non-linearity, removal of cause from effect, multiple endings (see John Fowles's The French Lieutenant's Woman amongst others), direct address to the reader - all of which is intended to emphasise the novel's status as artifice, not reality.
Not all works which can be defined as postmodern are that extreme. Many can simply be read as stories, though maybe told in a slightly unusual way. Alice Walker's The Color Purple, for example, is a series of letters from the protagonist, Celie, to God. Walker uses the old (and certainly predating the Modernist era) convention of the epistolary novel, but as the letter writer is a poor black woman, someone who would normally not be given the "authority" to write. And while that is going on, you can read the novel simply as a very moving story - no wonder it did so well.