Ah, quite the contrary. I like to describe postgenomics as genome enabled research. In fact it is kind of a fancy word to state that I apply high-throughput genomics (in silico as well as real lab), transcriptomics (mostly microarrays), proteomics (mostly whole-proteome mapping) and metabolome studies to try to understand cellular physiology. Or in other words, the application of genome data-dependent high-throughput techniques. Well, as you can easily see why I prefer to say "postgenomics" rather than typing all that stuff. I had specialized a bit in analyzing regulatory networks and cellular responses on the above given levels but have recently moved on to try my hands on single-cell analyzes.
Of course these approaches were not able to fulfill all the expectations when it was first thought of around the 90s. Much the same way as whole-genome sequencing was not the "golden bullet" one might have hoped it to be. Yet it has been established as a kind of own discipline, less due to the biological answers that are sought (as, obviously the human proteome project will have little overlap with whole-proteome mappings of, say, certain bacteria), but mostly due to the similarity of approach and way of dealing with the data (though as of yet, the data analysis part is not maturing as fast as the actual technical aspects). Hence there is a large overlap in this area with bioinformatical workgroups.
Interesting enough postgenomics does have a connection to systems biology, as it was (and is still) belived that the high-throughput techniques might in fact be a way to get sufficient quantitative data for modelling approaches.
Essentially the basic difference between postgenomics approaches and more traditional one is, in my opinion, the throughput of data and the way to deal with it.
As I am writing this post rather late between ending work and going home I will check back tomorrow whether I made any sense, or not.