Former City winger Adam Johnson netted the winner for Martin O'Neill's men but Mancini believes that in the build-up to the goal, Pablo Zabaleta should have been awarded a free kick after being challenged by Craig Gardner.
Defeat at the Stadium of Light has left the Premier League champions seven points behind Manchester United and Mancini slammed the match officials' display during his side's second league defeat of the campaign.
"The referee ate too much for Christmas. He was not in good form," said Mancini.
"He and the linesman, I think, after Christmas, it can happen to have a bad performance like today."
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“Today I thought he was excellent. It was good for him to score against his former team. He looked surprised that he’d scored the goal. He wasn’t sure whether it had gone in," O'Neill told TalkSPORT.
“For one so slim he’s actually got a fantastic shot on him and I think if he could get into those type of positions a wee bit more often but he’s striving to do that.
“I think we all accept that he hasn’t settled as quickly in the side as Steven Fletcher but there are signs there that he’s really coming in to the sort of form that we know he’s capable of."