After a flawless defensive display at Stamford Bridge, where the Premier League champions led through Willian's strike, Christensen's loose pass evaded Cesc Fabregas with 15 minutes to play.
Barca captain Andres Iniesta subsequently set up Lionel Messi to beat the otherwise untested Thibaut Courtois to earn the Catalans a crucial away goal to take into the second leg on March 14.
Conte left club captain Gary Cahill on the bench but the Italian said he did not regret selecting Christensen in the heart of a back three, the Denmark international flanked by Antonio Rudiger and Cesar Azpilicueta.
"It was a great performance, an incredible performance," Conte told a post-match news conference. "He is only 21 and it is great he can play with that maturity. He was one of the best players. He played a top game and I am very pleased for his performance.
"I don't remember a great save from Thibaut. They had the one chance in the first half with Paulinho and then the second half with [Luis] Suarez. I think we played a really good game and I must be pleased because my players made a great effort. They followed the plan, the programme we prepared.
"They showed themselves to be a really strong team, a fantastic team, but we showed that if we are ready to work very hard together defensively but at the same time when you continue to have the right feeling with the ball to create the chance to score I think that we can try to do something incredible at Camp Nou."
Conte did not make his first change until 83 minutes had been played, Alvaro Morata replacing Pedro, with Danny Drinkwater then coming on for former Barca midfielder Fabregas.
But Conte, who did not use his third substitution, with Olivier Giroud among the players left on the bench, reiterated that he felt Chelsea – who fielded a front three of Willian, Pedro and Eden Hazard – performed to a high standard.
"Without the mistake Barca were struggling to create a chance to score," Conte said. "We tried to exploit the situation. Don't forget we hit the post twice and we were unlucky. We gave 120 per cent.
"Our three strikers played very well and a fantastic game. Willian played really well against Hull [City in the FA Cup] and in the last three games we have scored eight times – seven with Willian, Pedro and Hazard. We must be pleased with the game, not the final result."