Gordon Haskett Research Advisors analyst Charles Grom said in the note that the cuts look deep on the surface but in reality, reveal modest reductions.
The average price of more than 100 products Grom tracked from last week declined by 1.2 percent as of Monday, but 78 percent of those products did not see any discounts, according to Tuesday's note.
Products with the greatest discounts came from the dairy and yogurt section (5.6 percent), according to Grom's note.
Those statistics come from a single store in Princeton, and Grom says the results indicate the market's initial reaction to Amazon's announcement may have been excessive.
"We will continue to monitor the situation going forward, but our initial checks suggest that Amazon's bark may be greater than its bite," the note said.
Whole Foods Market has Bergen County locations in Paramus, Closter, Edgewater and Ridgewood.
Click here to follow Daily Voice Hackensack and receive free news updates.