But Medhi Benatia fouled Lucas Vazquez in the dying moments, prompting referee Michael Oliver to award a penalty.
After the game, Buffon told reporters that "a human being can not destroy dreams like that at the end of an extraordinary comeback on a dubious situation", referring to Oliver.
Buffon faces an extension to the automatic one-game ban for his red card.
UEFA says the case against Buffon relates to "general principles of conduct" and his red card for confronting the referee.
Shipping Will Have Time to Adjust to Iranian Sanctions
Now it's up to the Iranians and other countries involved in the deal to help the world stave off that unnerving possibility. Italy has long-established political and economic ties with Iran, and is its main trading partner within the EU.
Buffon's emotion was in part put down to the fact that, after a long career in which he never lifted the European Cup, it may have been his final act in the Champions League.
He was sent off before Cristiano Ronaldo scored from the penalty spot to send Madrid through 4-3 on aggregate to the semifinals.
After the match, Buffon accused Oliver of having "a bag of rubbish" instead of "a heart" and claimed that he should "sit in the stands" and "eat crisps".
Despite not being directly involved in the foul on Lucas Vazquez, the former Italy global was dismissed by the 33-year-old Premier League official for his abusive reaction; which saw the shot-stopper furiously yelling and grabbing the referee in protest.
Also on Friday, UEFA dismissed an appeal by Atletico Madrid and coach Diego Simeone against a four-game ban for his conduct at the Europa League semifinal first leg at Arsenal.