Juventus are keen to take revenge on the side that beat them in the 2015 Champions League final but Allegri said the Turin giants would keep their eye on one challenge at a time.
Yet Barcelona coach Luis Enrique remains in bullish mood.
He had other chances to score before he finally got his second, six minutes from time, after more good work from Dybala in picking out Stephan Lichtsteiner, who crossed for Higuain to control and curl into the bottom right corner.
"We were coming off a couple of tough games and it was only natural we'd be a little exhausted, so in my view this was one of our toughest games of the season, as we had used up so much energy with [two clashes with] Napoli". So many players of my age had already won important trophies, I'm still trying to improve. Juventus are now top of the table, six points clear of second-placed AS Roma and seemingly headed for a 6th consecutive Serie A title. Barcelona will have the ball for a majority of the game. Juventus should be used to playing games like this. He'll have an intimate knowledge of the tendencies and strategies of the Barca front three, even though that kind of thing doesn't really seem to matter against players of their quality. This tie calls for a more disciplined approach. As of now, Alves is likely to feature at right-back in a back four which also features Bonucci, Chiellini and Brazilian Alex Sandro.
On offense, Juve will need to be efficient on the break.
Allegri has called for a "fearless approach" as Juve look for a crucial first leg advantage, writing on Twitter: "Calm, fearless and knowing what we're all about: coming next from Juve, a game that will leave all our fans in high spirits".
The fluency of Juve's all-star attack soon showed as Sami Khedira forced a low stop from Andrea Seculin with his firm strike, before the goalkeeper turned Paulo Dybala's rising shot over the crossbar and gathered a second effort from the same player.
This is a mouthwatering matchup between Champions League heavyweights. The two clubs come into this game on the back of radically different recent form.
Mario Mandzukic is set to be rested but treble-chasing Juventus were warned to focus on Chievo despite the looming visit of Barcelona in the first leg of their Champions League quarter-final.
"It's always good not to concede a goal when you play the first leg at home but that is going to be hard this time and it is likely they will score", admitted Allegri, even though his side have conceded only two goals in the competition.
"I am not annoyed by these comments, if anything they make me smile". Barcelona will surely be good for a few goals in the second leg, securing their passage to the semifinals in the process.