Madrid became the first team to win back-to-back trophies in the tournament's modern format with a commanding 4-1 win in Cardiff on Saturday.
Juve were deservedly level at half-time after Mario Mandzukic's wondergoal cancelled out Cristiano Ronaldo's opener, but the Serie A champions produced a listless display after the break to allow Zinedine Zidane's side to cruise to victory through further goals from Casemiro, Ronaldo and Marco Asensio.
It is the second time Juve have finished runners-up in the space of three seasons, with Barcelona having beaten them 3-1 in 2015, while they now hold an unenviable record of having lost their last five Champions League finals.
Writing on his Instagram page after the match, Bonucci conceded that it was a tough end to an otherwise successful season in which Juve won Serie A and the Coppa Italia.
"The disappointment is there, it exists. We thought and we believed that this would be the right time," said the Italy defender.
"Unfortunately, that was not the case. Congratulations to Real for the victory.
"However, I remain proud of being part of this group. We brought home two titles, doing something truly unique.
"A round of applause to you fans of the Old Lady, you were there, you always have been and always will be. In defeats and victories."
La delusione c'è, esiste. Pensavamo e credevamo che questa volta sarebbe stata quella giusta. Purtroppo non è stato così. Complimenti al Real per la vittoria. Resta però l'orgoglio di aver fatto parte di questo gruppo. Abbiamo portato a casa 2 titoli, facendo qualcosa di veramente unico. Un applauso a Voi tifosi che per la Vecchia Signora, c'eravate, ci siete e ci sarete sempre. Nelle sconfitte e nelle vittorie. #finoallafine #LB19 #atestaalta
The challenge facing Juve now is to dust themselves down and go again in 2017-18, with the clock ticking on an ageing team in Turin.