As it was, a brace from the Costa Rican, Paulo Wanchope, within the opening four minutes of each half and a fine low drive from Gary Rowett helped Derby's push for Europe.
Wanchope took his goals with real aplomb, his first a low cross shot, his second a neat lob. Rowett's 66th minute effort, powerfully driven into the bottom corner from 15 yards, was no more than Smith's men deserved for what was at times an exhilarating display.
Atkinson said: "We were dismal. We are the luckiest team in England today. To be fair, you don't get that much luck in a season, and I told the lads this at half-time and amazingly we were still in with a chance at that stage."
While Atkinson was angry with his own team's performance, he had nothing but praise for Derby. "They did everything better than us. It was one of the worst performances under me," he said.
"After watching them several times this season, I knew what they could do if you allowed them to get in amongst you. They are a good side, but we made it too easy for them. We were nowhere near as determined or tight as we should have been."
Jim Smith, the Derby manager, was delighted with the quality of his team's performance, especially as he was forced to do without the services of Dean Sturridge, who was recovering from a car accident.
"Our performance was as good as we've had over 90 minutes," he said. And with Derby are on the brink of challenging for a place in Europe he added: "It would be great for the club and everyone involved. We've got something to play for until the end of the season."
Goals: Wanchope (3) 1-0; Wanchope (49) 2-0; Rowett (67) 3-0.
Derby County: Poom; Rowett, D Powell, Stimac, Wanchope, Laursen, Carsley, Eranio (Hunt, 80), Dailly, Burton (Delap, 85), Baiano. Substitutes not used: C Powell, Willems, Knight (gk).
Sheffield Wednesday: Pressman; Atherton, Pembridge (Magilton, 69), Newsome, Walker, Carbone, Di Canio (Mayrleb, 69), Hyde (Booth, 54), Rudi, Hinchcliffe, Barrett. Substitutes not used: Oakes, Clarke (gk).
Referee: A Wilkie (Chester-le-Street).
Bookings: Derby: Dailly, Stimac. Wednesday: Atherton.
Man of the match: Wanchope.