Kenzo Goudmijin, Kayden Jackson and the outstanding David Ozoh got the goals as City were swept aside.
Warne said: "Really proud it was the best Derby performance I've seen since I've been here.
"I know scorelines can sometimes, but flatter we created a lot of good chances and it just felt more like my team than ever."
City had chances but could not find a way past Swedish goalkeeper Jacob Widell Zetterstrom who twice denied Sinclair Armstrong before Goudmijin scored his first goal for Derby.
Zetterstrom made another top save from Armstrong early in the second half and Derby took full advantage when Jackson followed up his winner against Middlesbrough two weeks ago with the second.
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