Dale keeper JoshLillis failed to hold a close range sidefoot from debutant Derbyshire as the striker's effort was deemed to have crossed the line before it had been cleared from the Dale goalmouth.
And they only had themselves - and their poor finishing - to blame, not least Butterfield who fired an early chance over, curled another effort wide of the post, saw another shot held by Rochdale goalkeeper JoshLillis and was inches off target with a header.