The Portuguese was gutted after goals from Gareth Bale, Marcelo and Cristiano Ronaldo in extra-time gave Real Madrid European glory for the 10th time
Diego Godin's first-half header looked set to give Diego Simeone's men the victory before Sergio Ramos nodded home in second-half stoppage-time, taking the tie into a further 30 minutes.
Gareth Bale punished the Spanish champions by heading in Angel Di Maria's rebounded shot before Marcelo and a Cristiano Ronaldo penalty put the result beyond any doubt at Estadio da Luz.
"We have given our all but, in the end, we had no strength," the Portuguese told La Sexta. "I'm very proud but very sad at the same time.
"We will continue giving our lives for this team."