Allegri has established himself as one of Italy's most talented coaches in recent years, initially getting his big break in 2010 when he joined AC Milan, whom he guided to a Serie A title in his first season.
Juve saw forward Paulo Dybala sent off for a second yellow card before Marcelo added Real's third away goal in the 72nd minute to all but end the contest ahead of the second leg back in Madrid.
Allegri has added fuel to the fire by confirming that he intends to move overseas for his next job once leaving the Allianz Stadium, telling The Telegraph: "Certainly".
Ironically, Allegri replaced Conte at Juventus four years ago and led them to the finals of the Champions League twice, while Conte failed to qualify for the last-16 in his final season. "You can only congratulate him for what he's doing at present".
He says he was not surprised to see Ronaldo produce such a sublime finish.
"We made a few mistakes, but it can happen when you face the best".
"They're absolutely frightening when there's an open pitch, they can reach the box in two or three passes so we'll have to be really attentive and we'll have to use our defence as a foundation to attack".
Juventus fans stood to applaud the effort, and Real Madrid head coach Zidane said: "You can say he's one of the most attractive players in the history of football. That's a real shame, but against some teams you have to be calm and congratulate them, because objectively they're a stronger side".
"It was a great game - it's not easy to win 3-0 here".
Speaking at his pre-match news conference, he said: "Of course, we have watched the final again several times, and I would say that the team, especially in Europe but also in Serie A, has improved a lot, especially in managing the hard moments during the match".