The Premier League champions came closest to breaking the deadlock in the first half despite surrendering 73% of the possession throughout the match, with Willian hitting both posts before the interval.
The Brazilian did eventually break the deadlock, but Barcelona levelled things up through Lionel Messi's away goal, leaving Conte bemoaning one defensive error from an otherwise "great" performance.
"We were very close to the perfect game. One mistake and we know very well when you make a mistake against Barcelona and players like Messi, [Luis] Suarez and [Andres] Iniesta you pay," he told BT Sport.
"It is a pity. I am very proud for my players. They followed what we prepared. It's a pity. Tonight we were a bit unlucky.
"I think when you play this game you must have a plan and respect the characteristics of the opponent. Our plan was really good. The effort of the players was great, we are talking about 1-1 and maybe we deserved more.
"I think in the second leg we have to play a game against Barcelona and we know his team is very strong and fantastic. The final result and qualification is open, it will be very difficult but our performance gives confidence to try and do something incredible."
Chelsea are now unbeaten in their last eight matches against Barcelona.