Juventus captain and Italy global Buffon was sent off for confronting Oliver over the 93rd-minute penalty decision.
He said that Oliver "has a rubbish bin where his heart should be" and went on to disparage the referee further.
Gianluigi Buffon said that he had no regrets over his outburst against the referees. But the content remains and I stand by all of it. "I could nut somebody - who knows". I felt defrauded of a night that can never be repeated'.
English referee Oliver then awarded a contentious spot-kick in added time after ruling Mehdi Benatia had bundled Lucas Vazquez over in the box. Cristiano Ronaldo scored the penalty and Juventus were gone too.
Should he decide to stay on, he will miss the first match, if not more, of next season's Champions League campaign with Juve. He left the pitch in ignominy, but his emotional response was understandable, if excessive: Juventus had overturned a 3-0 deficit at the Bernabeu and were on course to take the tie to extra time.
"I'm sure Oliver will have a great career in future, but he's too young to officiate a match like that".
The 40-year-old goaltender was red carded in his side's 3-1 victory over Los Blancos in the second leg of their UEFA Champions League quarterfinal clash at the Santiago Bernabeu on Wednesday, April 11. "I think the same is true of my teammates and the fans".
"To say that you cannot give that penalty in the 93 minute is not correct, but you must be 10 percent sure to give it, even if it is in the first minute".
BBC Sport reported on Sunday that Oliver's wife Lucy, a women's Super League referee, had her mobile phone number posted on social media after the game, which led to her receiving abusive text messages.
"Oliver was doing his job and hard to argue against his decisions".