Paulo Dybala struck two brilliant goals and Giorgio Chiellini headed a third goal to put the Serie A leaders in full control on a stunning night in Turin.
Barcelona had to overturn an even greater deficit against PSG, coming from 4-0 down after the first fixture with an incredible 6-1 victory at Camp Nou in the second leg, but Luis Enrique believes it will be hard for his team to repeat the trick.
"It was a difficult first half, very similar to the one in Paris, and the second was much better," Luis Enrique told Mediaset Premium.
"If you gift the first half, then obviously you're going to have problems.
"It's the second time this has happened. It's hard to think of a comeback, but we'll try to get back on our feet and put in a good performance in the second leg."
Champions League (@ChampionsLeague) April 11, 2017
Luis Enrique refused to lay the blame for Barca's loss at the feet of his players, insisting they had not been prepared well enough to face Juve, who are unbeaten in 22 home matches in European competitions.
"A coach does everything to help the team and prepare them, but evidently I did not," he said.
"We have to improve, learn from these mistakes, analyse the game carefully and realise where we went wrong.
"It's not good to pick on single players after a defeat. It's a defeat for the whole team, starting from myself."