"Aside from our determination, which is traditionally part of the Juventus identity, we are becoming more "European" by pressing, proving unsafe in attack and controlling the game more than we did in previous years".
Trailing 3-0 from the first leg, Barca managed only one shot on target as they failed to repeat their last-16 heroics when they overturned a 4-0 deficit to beat Paris St-Germain.
The story was strong and powerful ahead of Juventus battle but the eyes of Barcelona players and staff didn't hide the dearth of belief the Catalans can actually pull it away once again.
Playing in a two-man central defence with ex-Barcelona star Dani Alves and Alex Sandro as the full-backs, the pair helped the Serie A Champions to their fourth clean sheet in a row.
Allegri, however, said that Juventus could have made life easier for themselves if they had taken advantage of the space Barcelona offered them as the game wore on.
Allegri then added: "We haven't achieved anything yet, though". "It's a fantastic night for us".
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Juventus's outstanding display to knock Barcelona out of the Champions League will have the rest of Europe running scared of the Old Lady, defender Leonardo Bonucci said on Wednesday.
Allegri has instilled in his players an unwavering focus and a duty to never let their guard down.
Bonucci collected Messi's shirt at the full-time whistle after winning his individual battle with the Argentina superstar and insisted Juve are the team to avoid in the semi-final draw. You have to do your job and defend your colours with honour, but the taste is still there.
Buffon believes Atleti may be their worst match-up because they are not challenging for their domestic league title like the other two are. To put that in perspective, the entire Juventus team completed 12. After beating Barcelona, there is a very real sense that Juventus could emulate Inter Milan and win the treble.
"Big clubs will always look to add one or two players at the end of the season and the only one you would look at is (Andres) Iniesta, who is coming towards the end of his career".
"Overall they were the better team and deserved to go through", Pique told BeIN Sports Spain. "It's the right result and down to us as we have grown in conviction and personality: we are a team which is more and more European".
Atletico Madrid, Juventus, Monaco and Real Madrid will discover their fate for the last four at UEFA's headquarters in Nyon, Switzerland.