The Bianconeri entered the break level after Mario Mandzukic's brilliant equaliser had cancelled out Cristiano Ronaldo's 20th opener for Real. But Real struck twice in quick succession just after the hour mark in what Allegri conceded was "a tough 15 minutes" to all but end the final as a contest.

It was Juventus' fifth consecutive European final loss, despite only conceding three goals on the way to Cardiff's decider.

"I am very proud of what the lads achieved this season. We came here to win the trophy and didn't manage it," Allegri told Mediaset Premium.

"We played a really good first half and didn't make the most of our chances. [Miralem] Pjanic had a knee problem, Real Madrid raised the tempo and we had a tough 15 minutes.

"We conceded that goal with a deflection and then let go psychologically. We should've reacted and defended with nails and teeth, but this is another step we have to take in [the] future to learn from this and mature.

"Even if Real Madrid had a very good second half and have excellent players who can change the game at any moment, that second goal knocked the wind out of our sails.

"We should've reacted, but you can't do anything with ifs, buts and shoulds. Life gives us the opportunity to try again next year, so we must calmly analyse where we can improve as a team, in our football and in our mentality.

"They raised the tempo, as we were the ones pushing Real Madrid back in the first half, but in the second we couldn't play our way out of defence and they kept pushing us back.

"At that moment, we should've taken out the extra energy to push hard and keep the game open, as we know Real Madrid leave you the chances to score at all times, but we conceded the third goal and that was really damaging.

"We begin next season determined to have another great Champions League campaign, win the Scudetto and the Coppa Italia. We need to gather our thoughts, fire up our energy and fight back, because we can learn from this and improve."

Allegri, who had been linked with the Arsenal job before Arsene Wenger penned a new deal at the Emirates, insisted that the loss has only spurred him on to achieve his goals with Juventus.

"This acts as further motivation to reach the final again and hopefully win," Allegri said.

"The squad has everything it takes to do that, the club knows where we need to improve and adjust.

"[Gianluigi] Buffon and [Andrea] Barzagli will still be with us next year and they still have a lot to give us.

"Clearly we need to improve the team to achieve a higher level of technical skill -- but after the holidays we'll go back to work with a new stimulus. Football gives you the chance to go again next year."

Allegri started the postmatch news conference by reading out a statement after news broke of injuries to fans watching the final in Turin.

Fans were injured following a stampede at the city's Piazza San Carlo, which reportedly occurred when firecrackers were mistaken for the sound of gunfire.

The Bianconeri coach said: "I'd just like to say that we feel for what happened to our fans in Turin.

"There was an incident there and we're hoping not too many people were injured seriously and we are hoping that they get better very soon."