Muntari was booked for dissent after complaining to the referee about the abuse on Sunday and left the pitch in protest during stoppage time, leaving his team to play the last few minutes with 10 men.
The Ghanaian was shown a second yellow card for leaving the pitch without permission, which the Serie A's disciplinary committee confirmed had triggered an automatic one-match ban.
The committee also said no action would be taken against Cagliari because only around 10 supporters were involved in abusing Muntari.
"The gutless failure to not take action by the Italian authorities should not be allowed to pass," Kick It Out said in a statement on Wednesday.
"It's unbelievable that Cagliari escaped punishment as 'only 10' fans were involved. This situation should never be allowed to happen again.
Italy and other countries have struggled to stamp out racist chants at games. In 2013, the AC Milan team left the pitch during a friendly in the town of Busto Arsizio after home fans insulted midfielder Kevin-Prince Boateng, another Ghanaian.
Under guidelines introduced following that incident, the referee is supposed to alert the fourth official who should in turn contact authorities policing games.
(Reporting by Simon Jennings in Bengaluru; Editing by Richard Lough)
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