William Osula came off the bench to score the winner for the 10-man home team at St James' Park, putting a dent in United's push for Champions League qualification.
Former United midfielder Carrick, who took charge at Old Trafford in January, had won six and drawn one of his seven games in charge before Wednesday's trip to Newcastle.
He was also unbeaten during a previous interim stint at the helm, in 2021.
Jacob Ramsey's dismissal for a second bookable offence sparked a frenzied conclusion to the first half, during which Anthony Gordon put the home side ahead from the penalty spot before Casemiro restored parity.
But United failed to capitalise on their man advantage in the second period and Osula produced a moment of magic at the death, sprinting down the right before cutting inside and curling an unstoppable shot past Senne Lammens.