Two goals from Mario Mandzukic and another by Blaise Matuidi had put Juventus 3-0 up on the night and heading for extra-time after levelling the two-legged Champions League quarter-final at 3-3 on aggregate.
But Premier League referee Oliver awarded Real a late spot-kick for a Medhi Benatia’s foul on Lucas Vazquez, before sending off Juve goalkeeper Gianluigi Buffon for his reaction to the decision.
Cristiano Ronaldo converted the resultant spot-kick past substitute stopper Wojciech Szczesny to send Real into the last four and leave Agnelli fuming.
Juve also had a men sent off in the first leg when Paulo Dybala was dismissed and Agnelli 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 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 did PSG last season and Roma last night – proved 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.’
Agnelli went on to suggest that Pierluigi Collina, the UEFA chief in charge of assigning refs to Champions League matches, was so keen to prove that the organisation were not corrupt in favour of Italian sides that he has been deliberately placing anti-Italian officials in charge of Juventus, Roma and Milan fixtures.
‘We must stay calm and analyse the situation,’ said Agnelli. ‘I see a series of countries that implemented VAR and I saw incidents that went against Italian clubs recently, such as the foul on (Juventus winger Juan) Cuadrado, 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.
‘It’s not Juve, but Roma had penalties denied against Barcelona, Milan went out of the Europa League with Arsenal, us tonight. If it’s a technical problem because UEFA don’t have good enough referees, we can offer to help train them.’
Roma overcame Barcelona 3-0 on Tuesday to overturn a 4-1 first-leg loss and reach the last four of the Champions League.
Milan exited the Champions League in the round of 16, losing 5-1 on aggregate to Arsenal, who were handed a controversial penalty while the tie was poised at 2-1.