That made Ronaldo the second man to score in three finals, after Alfredo Di Stefano, who netted in five in a row for Real in the 1950s.
"It's another record and these players deserved it, me too because I scored two goals and finished as the top scorer in the Champions League".
Strikes in each half from Ronaldo made him the first player to score in three finals in the Champions League era, adding to his goals in the 2008 and 2014 showpieces for Manchester United and Real respectively.
"In the first half we played beautifully but they pushed the accelerator in the second half and we could not resist", Allegri, whose side had been bidding to become the eighth club to land the "treble" having won Serie A and the Copa Italia this year, told reporters.
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Cristiano Ronaldo scored twice as Madrid overwhelmed Juventus at the Principality Stadium to become the first team to retain the European Cup since AC Milan in 1990. "This is one of the best moments of my career - I have the chance to say this every year", he said.
"Second half we were clearly superior, we kept the ball, physically I think we won the game there as well. I prepared for that because things are won at the end of the season", Ronaldo said. [Gianluigi] Buffon and (Andrea) Barzagli will still be with us next year and they still have a lot to give us.
Real Madrid captain Sergio Ramos showed the best and worst of his game in the Champions League final on Saturday, finishing it by holding the trophy aloft minutes after his simulation led to a red card for Juventus substitute Juan Cuadrado. "Then we will get some rest and later we will start thinking about next season".
The 32-year-old believes Madrid were worthy winners and was happy to take another swipe at his detractors at the end of a season in which he has suffered boos at the hands of Madrid fans at Santiago Bernabeu and had his form questioned at times.
"The most important (thing) is that I again had an fantastic season, me and my team-mates have done the double".