The Millers` promotion charge faltered again as they slid to a third straight defeat following goals from Boro trio Peter Winn, Byron Harrison and Scott Laird.
Moore said: "For some reason we've switched off again too often, particularly at the end there. Coming here was always going to be a difficult test for us, but at times we made it too easy for them.
"We have to keep possession better and be much better in the final third. I've explained this to the players time and again, but the cutting edge just wasn't there again.
"We've dropped out of the top three now and it's entirely our own faults. We have to learn to defend better and show much more of what I know we are capable of.
"We're going through a miserable time of it at the moment, but it's up to us to put things right, and quickly."
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