It took Dybala just seven minutes to open the scoring, curling home a low shot from the edge of the six-yard box.
The Argentine himself was on target 15 minutes later when he found the bottom corner with a wonderful finish thanks to a smart cutback from Croatian striker Mario Mandzukic.
"It was a very hard first half, very similar to the one in Paris, and although we improved after halftime, the first half was full of problems".
Enrique was left frustrated by the similarity between Barca's poor start on Tuesday and their first-leg result in the previous round, when they lost 4-0 to Paris Saint-Germain on February 14.
Juventus boss Massimiliano Allegri is set to make major changes to his starting line-up for the Serie A match at Pescara on Saturday after the Italian champions' famous victory over Barcelona.More news: Bayern Munich Furious with the Referee: We Were Robbed
"I'm very happy and proud to be part of this team", the 23-year-old Dybala said.
"I think we put in a great performance, we made the most of the chances we had and it's a positive result for what we'll face at Camp Nou", Dybala told Mediaset.
"Juventus deserve credit, as everyone led to the defence by cutting off the passing channels, otherwise when the ball is at the feet of [Lionel] Messi, [Andres] Iniesta or [Luis] Suarez, you're going to possess problem".
"I take responsibility 101 per cent".
And, in another pop at his players, he labelled their first-half performance in Turin the "third half" from their 4-0 defeat in Paris in February. I can't get the first half out of my head. It means we are here, we had no reverence or fear for Barcelona, we played with our qualities.
"It felt like the third half of PSG vs Barcelona". "Even though I am optimistic, it's natural I also pass through moments when I grieve".