Mexes picked up a four-game ban following his conduct in last weekend's 3-2 defeat at Juventus, with the French defender sent off for two bookable offences despite his punch on Chiellini being missed by the referee.
Boateng believes that the retrospective action taken against Mexes was fair, imploring the centre-back to work harder on his temperament in big matches.
He told Football Italia: "Mexes is one of my best friends, he always wants to give his best, but he certainly exaggerated.
"The four-match ban is right. He has to calm down a bit, even if you can lose your head in games such as that one."
The 26-year-old has excelled since making a late summer switch to Schalke 04, scoring four times in seven appearances for the Bundesliga giants.