The best way to immediately dispute the notion that a “free market” solves all economic injustices is to pay attention to the quotation used in the question. Let me preface. One ought not to expect to reap the benefits of freedom without the implementation of freedom.
Indeed, by using quotations, the questioner also appears to correctly realize our version of “free-markets” violates the most basic principles of freedom. We have at best deployed an absolutism of freedom quite contrary to the relativity of freedom the world needs and deserves. Our market constructs are quite the opposite of free by any modest definition of freedom.
But be that as it may, even a marketplace in compliance with free-market principles will not solve all economic injustices for freedom is merely a proxy of dynamic relativity. And as long as there remain some marketplace participants intent on destroying or short-cutting the authenticity of the marketplace, there will be economic injustices.
The beauty of a marketplace, in compliance with real free-market principles as described briefly above, is that the governance of “bad apples” will be taken care of rapidly by other participants, and the minute they roar their ugly heads. Much better than government intervention bound to occur after the trust in the marketplace has already been damaged.
So, the freedom of a marketplace defines where the burden (and balance) of governance lies, and a marketplace in adherence to real freedom will systematically discourage bad actors from quietly doing significant damage, and way before it is all too late.