Real had looked certain to make the last four following last week's 3-0 first-leg victory in Turin, but Juve staged a sensational comeback in the return at the Santiago Bernabeu. The defense was sloppy without Sergio Ramos.
According to a report in Goal, Juve's frustrations came to a head in the tunnel following the match with "members of the team confronting the match officials and members of the Spanish side".
Madrid beat Juventus 4-3 on aggregate, courtesy of a Cristiano Ronaldo victor from the penalty spot in the 97th minute. The crowd got nervous when Mario Mandzukic added his second goal before halftime, and the unlikely comeback was almost complete when Blaise Matuidi scored the third about 15 minutes into the second half.
Ronaldo then stepped up and duly slotted the penalty past substitute goalkeeper Wojciech Szczesny with his team moving into the semi-finals 4-3 on aggregate.
The Italy defender was scathing in his assessment of referee Michael Oliver, who awarded a stoppage-time penalty and sent off goalkeeper Gianluigi Buffon for dissent as reigning champions Madrid advanced to the semi-finals 4-3 on aggregate despite Wednesday's 3-1 loss.More news: Trump asks USA trade officials to look into joining Trans-Pacific Partnership
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"I do not think of playing without Cristian, we have him and we are happy", Zidane said on Tuesday.
The Italian veteran, who is set to leave Juventus at the end of the season, was given a standing ovation from the home fans as he walked off the pitch in what is likely to be his last act in a long and eventful career in the Champions League.
Real, though, were shaky at the back, the channel between Marcelo and 21-year-old Jesus Vallejo regularly offering Juve hope. "We knew how to suffer until the end and that goal by Cristiano was crucial". His 41st goal of the season spared Real's blushes after Juventus had come from 3-0 down from the first leg to level the tie at 3-3.
Elsewhere, Bayern Munich and Sevilla finished goalless at the Allianz Arena, a result that saw the Bavarians go through to the last four.
Madrid star Ronaldo fired the resulting spot-kick home. "But Madrid are happy and in the semifinals". Navas should have done better, though, when Mandzukic rose above his marker to head Stephan Lichtsteiner's inviting cross through the grasp of the Real keeper. "That allowed their team to grow and it made things hard for us".