Carvajal screamed at the Slovenian official after Eduardo Camavinga's controversial dismissal cost his side any chance of progression.
The outburst, captured by Movistar Plus cameras, came as Vincic sent Camavinga off for a second yellow card, ruling that the Frenchman had wasted time by holding onto the ball. Luis Díaz scored for Bayern moments later to make it 3-3 on the night and 6-4 on aggregate, effectively ending the tie. Carvajal, who did not play a single minute in the match, leapt from the bench and confronted the referee directly.
"It's your fault! It's your f***ing fault!" Carvajal shouted at Vincic, repeating the words four times. The Real Madrid captain also directed his anger at the fourth official, who at that moment was engaged in discussion with another member of the bench.
Defender Antonio Rüdiger also made his feelings clear after the final whistle, though in more restrained terms. "You saw it, didn't you?" he said as he left the stadium at pace. "Seriously, it's better that I don't say anything. Have I ever seen anything like that? Oof..." He refused to say another word.
Bayern ultimately won 4-3 on the night and 6-4 on aggregate to reach the Champions League semi-finals, where they will face Paris Saint-Germain. Real Madrid are eliminated, ending a second consecutive trophyless season.