Jason Puncheon had put the Saints ahead inside seven minutes before Hart fumbled Rickie Lambert’s shot to allow Steven Davis to double the home side’s lead.
Edin Dzeko scored just before half-time, but Gareth Barry’s own goal restored Southampton’s two-goal advantage and ultimately sealed City’s third loss of the season.
Hart has been guilty of a series of errors in an indifferent season for the England international, and Mancini expressed his displeasure with the shot stopper’s form.
“Joe has made too many mistakes. He has not been good enough,” Mancini told the Sun.
“It was a really bad mistake from Joe.
“It was not good enough. It’s not strange because he’s done a few mistakes this year.”