Poppers criteria is a useful one, but like many criteria operating on the metaphysical field its only a beginning. (I say its metaphysical because is his theory itself falsifiable? It isn't of course, and that should give us pause in denying metaphysics).
Joan Robinson, in The Philosophy of Economics writes:
The hallmark of any metaphysical proposition is that it is not capable of being tested. We cannot say in what respect the world would be different if it were not true, the world would be just the same except we would be making different noise about it. It can never be proved wrong, for it will roll out of every argument on its own circularity; it claims to be true by definition of its own terms. It purports to say something of real life, but we cannot learn nothing from it.
She agrees with Popper, and alludes to him
Adopting Professor Poppers criterion for propositions that belong to the empirical sciences, that they are capable of being falsified by evidence, it is not a scientific proposition.
Yet metaphysical statements are not without content. They express a point of view and formulate feelings which are a guide to conduct.
Metaphysical propositions also provide a quarry from which hypotheses can be drawn. They do not belong to the realm of science but yet are necessary to them. Without them we would not know what it is that we want to know.
She points out
Perhaps the position is different in the respectable sciences [meaning the physical sciences], but so far as the investigations of psychological and social problems are concerned, metaphysics has played an important, perhaps indispensable role.
Since Robinson didn't know the physical sciences - its worth pointing out that the Newtonian conception of space as homogenous, absolute and everywhere the same, sounds quite close to the adoption of a Parmenidian monism in this physical context; and the historical development of atoms (adopted by Newton for his corpuscular theory of light) by Democritus was forced by the challenge that Parmendian monism had on the conventional understanding of change in the world.
Its worth also pointing out that religions, music and the arts are not falsifiable and encode metaphysics; they are meaningful, though not universally so. The correct scientific disposition towards them, is rather than dismissing them out of hand as not encoding verifiable principles; it is to understand their importance - that is anthropology in its widest sense - phenomenological rather than structural.