The Bianconeri boss was infuriated with referee Davide Massa's decision to dismiss the goalkeeper, although he praised his side's character for fighting back when down to 10 men.
The Bianconeri captain brought down Miroslav Klose after the German was put through on goal, prompting match official Davide Massa to brandish a red card in addition to awarding a penalty, which was converted by Antonio Candreva.
Fernando Llorente ultimately salvaged a point for the Turin giant, though seeing his side go down to 10 men infuriated Conte enough to declare his abstinence from future press conferences.
"It’s disappointing there’s this rule, because I think a penalty is punishment enough without the need for a red card," the 44-year-old told reporters after the match. "I’ve said that for years, regardless of whether it’s in our favour or against, because it ruins the game. Sometimes the referees give a yellow card, sometimes a red, so it’s never really clear.
"I will not speak before the Inter game [next week], nor before any other match for the rest of the season."
Despite his frustration, Conte still reserved praise for his team given the way they fought back to secure a point.
"We wanted to win, both with 11 men and with 10. What we try to drill into the players is a winning mentality and these lads know full well every game must be played to win," he said. "We picked up a point and I think the team proved again tonight why they are top of the table. We never gave in, continued to play football and tried to win the game despite going down to 10."
The draw extends the Italian champion's lead at the top of Serie A to nine points, with title rival Roma due to travel to Hellas Verona on Sunday,