"This evidence suggests that starchy USOs were a regular part of the Neanderthal diet at Payre from MIS 8/7 onwards. These results corroborate the recent evidence of starch grains in Neanderthal dental calculus at Spy and Shanidar  and demonstrate that Neanderthal consumption of plants was routine as early as MIS 8/7." This study also found evidence that Neanderthals captured fish and birds for food, not only large mammals.
"Functional analysis of stone tools at Payre further bolster the case that Neanderthals had a broad-based diet that included starchy plants, large animals, fish, and possibly birds. The acquisition of fast-moving small prey items such as fish and birds are often seen as exclusively the domain of modern humans and their capture is often linked to a presumed cognitive superiority of modern humans."Perhaps "modern humans" do not exhibit "cognitive superiority" to Neanderthals, who in fact on average sported brains larger than modern humans (1600 cubic cm for Neanderthals, 1400 for modern humans).
Consumption of starches would exert a selection for increased production of amylase, the salivary enzyme that digests starch. We now have evidence that hunter-gatherers inhabiting the regions of Luxembourg and Sweden about 8000 years ago had "high numbers of amylase genes in their genomes":
"An international consortium led by researchers from the University of Tübingen and Harvard Medical School analyzed ancient human genomes from a ~7,000-year-old early farmer from the LBK culture from Stuttgart in Southern Germany, a ~8,000-year-old hunter-gatherer from the Loschbour rock shelter in Luxembourg, and seven ~8,000-year-old hunter-gatherers from Motala in Sweden. In order to compare the ancient humans to present-day people, the team also generated genome-wide data from about 2,400 humans from almost 200 diverse worldwide contemporary populations."According to current ideas, the European hunter-gatherers of 8000 years ago were (like modern Europeans) descendants of Neanderthals who married H. sapiens when the latter entered Europe from Africa about 60,0000 years ago.  It is estimated that between 1 and 4 percent of the DNA of modern Europeans and Asians is uniquely Neanderthal.
"Both the hunter-gatherers as well as the early farmers displayed high copy numbers of amylase genes in their genomes, suggesting that both populations had already adapted to a starch-rich diet. " 
In combination these studies indicate that European hunter-gatherer ancestors had been gathering, processing, and eating starches in large enough quantities to select for higher numbers of amylase gene copies for a likely minimum of 9,680 generations before they encountered any farmers.
1. Hardy BL, Moncel M-H (2011) Neanderthal Use of Fish, Mammals, Birds, Starchy Plants and Wood 125-250,000 Years Ago. PLoS ONE 6(8): e23768. doi:10.1371/journal.pone.0023768
2. Universitaet Tübingen. "Europeans descended from at least three, not two, groups of ancient humans." ScienceDaily. ScienceDaily, 17 September 2014.
3. National Geographic. Why Am I Neanderthal?