Barca's Luis Enrique failed to win for the first time at home in Europe during his three-year reign as Juve held their hosts at bay to progress to the semi-finals on the back of a stunning victory in the first leg in Turin.
Allegri's men restricted Barcelona to a single shot on target in Thursday's (AEST) second leg and the coach praised the solidity of his side as they earned revenge for their final defeat to Barca in Berlin's Olympiastadion two seasons ago.
"Barcelona failing to score goals over two legs is almost unheard of," Allegri told Mediaset Premium.
"The players need to realise that they can do even better and we are slowly improving. We must not get ahead of ourselves, but it's right to feel enthusiasm and tomorrow we need to focus on Serie A.
"I am happy with what the lads are doing, but the key is not to maintain current form, instead we are aiming to improve it.
"Everyone was extraordinary tonight and when Andrea Barzagli came on [for Paulo Dybala in the 75th minute] it felt like we could have played for a whole day and not conceded."
Juve remain on track to win the treble, with Allegri's men eight points clear at the top of Serie A and in the final of the Coppa Italia - where they will face Lazio - and he insists there is more to come from his team.
"We have to compliment the lads for all they are doing this season," he said.
"It's a step forward, a deserved qualification against a top-level opponent.
"We did very well defensively, less so in attack where we failed to make the most of very promising counter-attacks. We were under the normal amount of pressure here, but it was a decisive step on the road to Cardiff.
"We should have been calmer and sharper when spreading their play, but it's not easy to do that here, as Barcelona are a completely different team at home. They move the ball around so quickly and only a great Juventus could have qualified."