Barcelona did create opportunities but Lionel Messi was denied by Gianluigi Buffon in the Juventus goal and neither Luis Suarez nor Neymar could capitalise on the chances that came their way.
But Allegri guided the team to its first Champions League final in 12 years as well as back-to-back league and cup doubles.
However, the Juve stalwart has urged his team-mates to keep pushing for glory, telling BT Sport 2: "We're very happy with these small victories but what we really want to do is go all the way. We did very well defensively, less in attack because we failed to make the most of some very promising counter-attacks by missing some simple passes".
However, it wasn't enough as Barcelona's fearsome attack sputtered at the Camp Nou against the defending Italian champions.More news: Sarin or similar used in Idlib attack: chemical weapons watchdog
Following their performances against Barcelona in the UCL, the FC crew explain why Juventus are now the favourites to win it all.
"We showed great unity and solidarity". "Tonight they all had a great match, we could have played for an entire day without conceding".
Messi, Neymar and Pique played the full 90 minutes of the game against the Italian giants as the Catalans were trying to turnaround a 3-0 deficit from the reverse fixture played in Turin last week.
The surprise team in the final four, Monaco now lead Ligue 1 in France, which could mean an 8th league title for them and a first since 2000.
Yet veteran keeper Buffon admits the prospect of facing Diego Simeone's Atletico is one Juventus would rather not face in the last four.More news: Anaheim Ducks douse Calgary Flames 3-1 to complete playoff series sweep
He almost delivered another important and rare goal, but when the right-back's effort flew just wide 20 minutes from time so did Barcelona's hopes.
"There are four sides left in the Champions League, who have proved on the pitch they are the best in Europe".
The Old Lady were exceptional as they saw off Barcelona over two legs in the quarter-finals. It's down to us now, our destiny is in our own hands for whether we can improve. We must not get ahead of ourselves, but it's right to feel enthusiasm and tomorrow we need to focus on Serie A.
"We haven't achieved anything yet, this match wasn't a goal but a step towards the final in Cardiff", Allegri said.More news: Man arrested over Borussia Dortmund team bus attack
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