Gylfi Sigurdsson’s first of the season broke the deadlock in the 28th minute before Dominic Calvert-Lewin scored twice, his second coming moments after Millers substitute Will Vaulks’ 86th-minute header had raised hopes of a late comeback.
Warne said: “I don’t look at my players as first-team players or reserves, they are much of a muchness.
“I don’t regard making all those changes as weakening the team.
“It isn’t like I’ve been offensive to the cup, I’ve got another big game Saturday.
“I was intending to throw the kitchen sink at them in the last 20 minutes and, at 2-1, it looked like I was a fantastic tactician.”