The importance of plot is complicated when considering modernist literature and the movements that came after it. Works like like Mrs. Dalloway, Ulysses, and Naked Lunch are bare for any real "plot" in the normal sense. Modernism was in many ways a challenge to the primacy of plot and structure, often by making things more mundane or dealing more directly with people, where then postmodernism challenges this by losing even that structure quite frequently (like Naked Lunch, which is frequently cited as the first postmodern novel and written with William S. Burrough's cut up technique). Modernism shot to heighten the use of subjectivity in literature, making the stories focus on the characters as they went through their lives with no climax or normative structure, per say, but with some structures maintaining. Modernists made literature about every day ordinary people, whether Jane Austen's Emma or Flaubert's Madame Bovary, the emphasis was on telling their stories which didn't necessarily have the normal idea of a plot as we see it in, for example, Shakespeare or Marlowe.
Plot, it should be noted, isn't the same as a story. A plot is forward trajectory usually holding a structural form. Even modernism, the postmodernists would argue, ossified into having a very particular form in which the story could occur. Postmodernism more than modernism is the explosion of plot with a type of playfulness, awareness of the book as writing, and metatextuality. This isn't to say that postmodernist works lack plots but that the plot isn't particularly important to them as a set of concerns. Indeed, postmodernism is the dissolution of form. Postmodernist still tell stories but to apply to them a necessary plot structure is where things get very tricky.
This all isn't to say that plot is, strictly speaking, unimportant. Plot matters as it is audience expectation. There would be nothing for the postmodernists to respond to if plot were unimportant. One can say that they apophatically prove the importance of plot by their negation. Plot's not unimportant and most works you interact with will still follow a plot structure. To see where plot still has a stranglehold over story, look at film. Though there are your Terrence Malicks and Charlie Kaufmanns playing with the structure of film, if you go to see a film by Steven Spielberg or Zack Snyder or Kathryn Bigelow, you'll usually find a very rigidly defined structure of how a screenplay must work along audience expectations. Stories have to fit the plot structure rather than the natural flow of the story to the point that with most action movies you can time out action set pieces regardless whether they make sense (which you can even find with Star Wars: The Force Awakens, for a good recent example of a plot-mandated action scene interrupting the flow of the story). This might be a parasitic vision of the plot but, well, that's structures for ya.
Plot is necessary even in its negation because it is what we are trained to read by most of the narrative we interact with on this planet. X happens, leading to Y, causing Z. Action will rise, action will fall, the story will have a tidy and natural conclusion. Even now in the century since postmodernism really sunk its claws into the world and unifying form of plot ebbs out of some of the most vaunted literature, plot matters because its what we expect and how we read.