The Millers' three-year stay in the second tier of English football came to an end courtesy of a 1-0 home defeat to promotion-chasing Fulham with seven games of the season left to play.
The club have managed just four wins all season and Warne, who took caretaker charge in November, said that he shoulders the "blame" of their relegation.
"There's a little bit of embarrassment," he told reporters after the game. "I took the reins a few months ago and I haven't been good enough to get the results to keep us up and that is on my head. The performances have been okay at times but we haven't got that strength in depth. That's my fault, it's not anyone else's.
"I don't think anyone thought before today that we would stay up. We weren't going to win eight on the spin. So to have 'relegated' next to our name isn't too much of a shock.
"Other people have inherited similar situations and have done better. I am the one who takes it home and doesn't sleep. I take that blame. In my eyes, I have done the best that I could, but other people might disagree."
Next up for Warne's side is a home encounter with seventh-placed Sheffield Wednesday on Tuesday night.