Speaking after the match Agnelli accused Oliver of "total chaos," questioning why VAR had not been used in the Champions League as yet.
"I see a series of countries that implemented VAR and I saw incidents that went against Italian clubs recently, such as the foul on Cuadrado, AC Milan at Arsenal and Juve tonight, proving we absolutely need VAR in the Champions League.
"This isn't about one or two points, but rather going forward in a massive tournament that brings so much money and prestige. We can't allow these incidents to occur.
"For some reason, the vanity of the refereeing designator is trying to scientifically prove he is unbiased and keeps assigning referees who are against Italian clubs."
Cristiano Ronaldo converted a 97th-minute penalty for Real to win it
Agnelli continued to slam referee Oliver, saying he lacked understanding of the moment, and should have understood the tie better following Paulo Dybala's sending off in the first leg a week ago.
He said: "Players make mistakes, so do referees, but this official completely lost control of the situation. A referee in Madrid for the quarter-final must have seen the first leg, realise the (Paulo) Dybala red card was excessive and understand the various situations.
"The referee tonight was in total chaos. It's a pity, the performance of the boys remains, we confirmed - as PSG did last season and Roma last night - you can come back from 3-0 down to turn things around. Incidents happen, the referee didn't understand the moment at all.
"The most important thing is we have the technology, it exists and is in use, so we have to bring it into the Champions League. The referee tonight, when he sees it back, will be the most disappointed person here to realise what happened."