This is put a bit more bluntly than anything Hayek says, but I do think there’s a strand of it running through some of his arguments:
What Rawls doesn’t see is how [a society based on the Difference Principle] would create conditions for an uncontrolled explosion of resentment: in it, I would know that my lower status is fully “justified,” and would thus be deprived of excusing my failure as the result of social injustice. Rawls thus proposes a terrifying model of a society in which hierarchy is directly legitimized in natural properties, thereby missing the simple lesson of an anecdote about a Slovene peasant who is given a choice by a good witch: she will either give him one cow, and to his neighbor two cows, or take from him one cow, and from his neighbor two cows – the peasant immediately chooses the second option. (In a more morbid version, the witch tells him: “I will do to you whatever you want, but I warn you, I will do it to your neighbor twice!” The peasant, with a cunning smile, asks her: “Take one of my eyes!”)
Friedrich Hayek knew that it is much easier to accept inequalities if one can claim that they result from an impersonal blind force, so the good thing about “irrationality” of the market success or failure in capitalism (recall the old motif of market as the modern version of the imponderable Fate) is that it allows me precisely to perceive my failure (or success) as “undeserved”, contingent… The fact that capitalism is not “just” is thus a key feature that makes it palpable to the majority (I can accept much more easily my failure if I know that it is not due to my inferior qualities, but to chance).
I don’t think anyone would (or should) seriously try to justify a market society on these grounds, but it seems psychologically accurate. Suffering an injustice at least comes with the consolation of indignation; a misfortune you genuinely believe to be perfectly just becomes far harder to bear.
Update: As commenter Tim notes, Zizek is also taking substantial liberties in characterizing the Rawlsian view, presumably for dramatic effect. The “worst off” are not some specific set of people doomed to misery by dint of their essential characteristics—who is in the group will depend on the specific set of rules and institutions selected. And it is Zizek’s own somewhat melodramatic gloss to say that in a Rawlsian society “hierarchy is directly legitimized in natural properties.” The intuition underlying that characterization, I’m assuming, is that in practice the typical effect of the difference principle will be to license disparity in incomes as an inducement for people with exceptional natural talents and capacities to bring them to bear. To be sure, you might equally say this is the point of the market society as well. But I think the psychological effect Zizek’s talking about depends to some extent on how obviously the social distribution is “patterned” (to use Nozick’s word) with a particular end in mind. The “natural hierarchy” stuff is actually somewhat behind the point, I suspect. It stems, really, from the implicit message: “In this best and fairest of all possible worlds, this just distribution that we scrupulously seek to enforce precisely for your benefit, you are nevertheless at the bottom of the ladder.” Maybe not, of course. People might still point to the ultimately “lucky”distribution of “natural endowments” or the inescapable environmental differences that dispose them to make effective use of those endowments. But it would seem to require a good deal of reconstruction of the way non-philosophers think about desert.