The triple punishment follows when the referee dismisses a player for an offence in the penalty area which he judges has denied an attacker an obvious goalscoring chance.
On Tuesday Manchester City F.C. defender Martin Demichelis was sent off for lunging in on his Argentine compatriot Lionel Messi of FC Barcelona and on Wednesday Arsenal F.C. goalkeeper Wojciech Szczesny was dismissed for clattering into Bayern Munich's Arjen Robben.
Both City and Arsenal F.C., reduced to 10 men for sizeable periods of their games were both beaten 2-0 at home by their opponents, making their progress in the competition unlikely.
Arsenal F.C. manager Arsene Wenger said that Italian referee Nicola Rizzoli had "killed the game" by sending off Szczesny.
"For 15 years we have been trying to change this rule. All the technical committees of UEFA and FIFA are against this but when it has gone to the International Board it doesn't change," Platini told a news conference on Saturday before the draw for the qualifying rounds of Euro 2016.
"Arsene Wenger said the referee killed the game but the referee had no choice - he has to respect this stupid rule."
UEFA's executive committee has proposed the issue is included on the agenda at next week's meeting of the International Football Association Board (IFAB), the game's ultimate law-making body.
"I am against it, and I want it to be changed," Platini said.
He has previously outlined other possible sanctions and he would also prefer the referee to have more discretion and that the award of a penalty does not automatically mean he has to issue a red card.
"I would change the system of cautions," he said in December.
"I would do it like in rugby, where the perpetrator would be punished by being off the pitch for 10 or 15 minutes of the game.
"That means the team they are facing would benefit in the same match.
FIFA president Sepp Blatter will chair next week's IFAB meeting in Switzerland and he has a different view from Platini, maintaining the sanction is a fit and proper punishment.
The IFAB, comprising four voting members from FIFA and four from the British associations, needs a 75 per cent majority for a law to be changed.
However, UEFA is pressing ahead with its plans to try to have the law amended.
"The Executive Committee has asked IFAB to address the issue and clarify the situation at their next meeting so that there are no more red cards for fouls committed inside the box," general secretary Gianni Infantino said.
"We need to resolve the issue of the 'triple punishment' once and for all. Everyone is talking about it and feels it is an injustice."