Goals from Mario Mandzukic and the star of the tie Dani Alves were enough to see off the Ligue 1 leaders 2-1 at Juventus Stadium, backing up their win in the principality last week.
Captain Gianluigi Buffon said post-match that reaching the final would mean nothing without victory in Cardiff and Allegri too espoused the importance of seeing out a first treble by an Italian side since Jose Mourinho's Inter after being denied by Barca in 2015.
"Gigi is right, we are in the final and must try to win it," Allegri told Mediaset Premium. "Hopefully this is the right year. I think Juventus have a very good chance of winning.
"We need to be more concentrated, keep the ball better, but there are important games over the next month and we have to get the result against Roma [where a point will secure the Serie A title] or risk putting the Scudetto back in doubt. There's the Coppa Italia final with Lazio too."
He added: "I am glad for the lads, they reached the final, but from tomorrow we have to focus, because we haven't won anything.
"I don't need to take credit for anything. I do my job. I do it with enthusiasm and calm. What I care about is using the quality at my disposal to get results.
"I really enjoy coaching, that is what makes me relax. When the stress sets in and I no longer enjoy it, that's the time to change."