Derrida generally resisted labels, and in particular he resisted the label of post-structuralism because his ideas were derived from structuralism—différance arising from Ferdinand de Saussure's linguistics—and, in point of fact, deconstruction only makes sense as long as it forms an extension of the structuralist approach, i.e. is within the bounds of a structuralist conceptual framework. For Derrida, structuralism was not completely wrong, it just had limitations like every other school of thought. Without structuralism, Derrida's work does not make a great deal of sense.
By saying that deconstruction is antistructuralist he is essentially creating a binary opposition between structuralism and deconstruction, and so it would never be post-structuralist, because it depends on its opponent; even if it does dismantle and criticise structuralism, without structuralism it is nothing.
post- would imply that structuralism was dead and buried, but this would be the last thing Derrida would say. Indeed, I imagine he would have rejected the use of
post- for any school of thought in philosophy, because it would imply that what came before was irrelevant or inferior, which would stand in opposition to his idea that philosophy is essentially a genealogy, a taxonomy of ideas in which every idea or school of thought is significant and serves to define its precedents and antecedents.