Chelsea looked set to secure a 1-0 win in first leg of their Champions League last-16 tie before Andreas Christensen played a loose pass into the path of Andreas Iniesta, who teed up Lionel Messi for the equaliser.
Willian had fired the hosts into a deserved lead with an exquisite finish after the break and Conte believes his side were “unlucky” not to win.
“We were very close to the perfect game,” he said after the final whistle.
“One mistake and we know very well when you make a mistake against Barcelona and players like Messi, Suarez and Iniesta you pay.
“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.”
The away goal means Barcelona head into the second leg on March 14 as favourites to progress to the last eight.
Chelsea midfielder Cesc Fabregas believes it would be a “suicide mission” to attempt to defend at the Nou Camp.
Conte admits his side are the underdogs but hopes they can take the positives from their showing at Stamford Bridge.
“I think in the second leg we have to play a game against Barcelona and we know his team is very strong and fantastic,” he said.
“The final result and qualification is open, it will be very difficult but our performance gives confidence to try and do something incredible.”