Phillips made an instant impact when brought on as a second-half substitute and forced the spot-kick converted by Craig Gardner when challenged by Patrick Vieira.
But Mancini felt the 37-year-old had gone to ground too easily as his team suffered another dent to their fading title hopes. They are now eight points behind leaders Manchester United and have played a game more.
City twice led through Carlos Tevez and Aleksandar Kolarov but were pegged back by Nikola Zigic and Craig Gardner.
Mancini said: "It was a disappointing result for us and we can't keep conceding two goals every game. It is impossible to win if you do that every time and the gap at the top at this moment is too much.
"But it isn't a penalty. It is nothing. It is impossible for that to be a penalty. He dived, the player (Phillips). I don't understand how the referee gave the penalty. When he loses the ball, he goes (down). That decision was costly for us. We didn't play well but it was not a penalty."