The Rams went into the final game of the season holding a two-point lead over Peterborough United, with goal difference ensuring that a point was realistically required at Hillsborough.
However, as Peterborough went in front during the early stages at Barnsley, Derby were second best versus Sheffield Wednesday and conceded just before the break through a Michael Smith penalty after Curtis Davies had been sent off.
Jack Taylor doubled Peterborough's lead against Barnsley, adding to Jonson Clarke-Harris's opener, and Derby were unable to find the equaliser that they needed to avoid missing out by a solitary point.
Sheffield Wednesday will now face Peterborough in the playoff semi-finals, with Barnsley and Bolton Wanderers squaring off in the other fixture.
Meanwhile, Cambridge United have survived in the third tier courtesy of a 2-0 triumph over Forest Green Rovers, Harrison Dunk and Sam Smith getting on the scoresheet in the first half.
MK Dons would have stayed up instead had they defeated Burton Albion, but they were held to a goalless draw at the Pirelli Stadium.
Accrington Stanley have also been relegated, despite overcoming Oxford United by a 2-1 scoreline, while Morecambe will join them in League Two after losing 3-2 at Exeter City.
At the top of the table, Plymouth Argyle were crowned champions as they came from behind to record a 3-1 triumph at Port Vale.
Ipswich Town finish three points adrift of the title rivals after being held to a 2-2 draw at Fleetwood Town, the Tractors Boys having to consolation of moving past the 100-point mark.