DERBY County's next opponents, Carlisle United, opened their League Two campaign with a 1-0 home defeat to newly-promoted Luton Town.
The Rams take on Carlisle at Brunton Park on Monday night in the first round of the Capital One Cup.
The Cumbrians, relegated from League One last term, entertained the Conference Premier champions on Saturday in front of a crowd of 6,766.
Mark Cullen scored Luton's winner after half an hour.
