The Millers went two down in the first 20 minutes before Adam Kimberley scored from the penalty spot after Reuben Wiggins-Thomas was fouled.
The home side restored their two goal advantage just after half-time with a penalty of their own and although Ryan Whitehurst pulled one back with a header from an Alistair Asher cross, Carlton couldn't force an equaliser.
Photos will be on site tonight and a brief match report will appear tomorrow.
The Millers are next in action on Thursday at Basford Utd. Photos and team details would be much appreciated as I won't be there.