The Black Cats appeared to be moving to within four points of the Champions League places after Asamoah Gyan's ninth goal of the season put them 2-1 up early in the second half.
But Huth claimed an equaliser seven minutes from time after Carew had cancelled out Kieran Richardson's second-minute opener just after the half-hour, and the German then slid home the winner in stoppage time to stun the visitors.
"They are fighting over it as we speak but it doesn't matter to me," said the Potters boss.
"Robert is desperately disappointed with the two goals we have conceded and obviously he is going to try to claim the two he claims he scored.
"I have no problems with that at all. It makes no difference, as long as we scored."
Source: PA
Source: PA