Bolton look set to be without Nicky Hunt for the start of the season after the full-back sustained medial ligament damage in the defeat at Pride Park. Hunt was forced off just before half time and boss Sam Allardyce told the club website: "We'll know more about his injury in the next 24-48 hours."
Inigo Idiakez gave Derby the lead with a free-kick and 17-year-old Giles Barnes sealed the win from close range.
Derby's new signing Steve Howard, a �1m capture from Luton, lasted 73 minutes.