The hosts were 4-0 ahead by half-time through a brace from Gary McSheffrey, Dele Adebola's individual effort and Stern John's header.
The visitors struck again through Paul Peschisolido's low shot but substitute Andy Whing's superb half-volley gave Highfield Road the perfect send-off.
Derby manager George Burley:
"For the first 10 or 15 minutes we looked comfortable but once they got their first goal the floodgates opened.
"Our defending was shocking and we gave away bad goals.
"But we have to take it on the chin, bounce back and make sure we are back in the groove when we play our final game of the season next week."
Coventry: Steele, Duffy, Page, Staunton, Hall, Jorgensen (Whing 67), Doyle, Hughes, McSheffrey (Morrell 78), Adebola (Benjamin 73), John.
Subs Not Used: Pressman, Goater.
Goals: McSheffrey 20, 29 pen, Adebola 37, John 40, 55, Whing 68.
Derby: Camp, Kenna, Konjic, Johnson, Makin, Idiakez, Taylor (Peschisolido 30), Bolder, Bisgaard, Tudgay (Junior 66), Smith.
Subs Not Used: Miller, Jackson, Huddlestone.
Booked: Konjic, Johnson, Idiakez.
Goals: Bolder 51, Peschisolido 63.
Ref: M Fletcher (Worcestershire).