Just convert your BED file to SAF and use FeatureCounts to quantify your BAM file over the features of your interest. Make sure your "BED" regions are not repeats or blacklisted on ucsc browser.
If you dont have coordinates of "unannotated" region, bin the genome into "n"KB bins and quantify your BAM file. This is been implemented as CSAW. Once your have the abundance from CSAW, intersect them with all known annotations and get the unannotated regions that show higher signal.