According to Platt, the Italian was extremely disappointed by both his side's performance and the display of referee Lee Probert, who awarded City a free kick when it should have been a penalty late in the game.
"Roberto Mancini is angry as you can imagine. He is taking stock of the situation and does not want to say things that would get him in trouble," Platt told BBC Sport. "He is angry about everything in general. We got outworked by Everton, but there is no doubt in my mind about the handball.
"It was not even on the line of the area, people can draw their own conclusions from that. Perhaps we could have got a bit more out of it if that decision had gone for us."
The result has left City 12 points behind leaders and rivals Manchester United, who will play their game in hand against Reading this evening.