The Blaugrana squandered a succession of gilt-edged opportunities during the game in west London and were punished for their profligacy by Blues forward Didier Drogba.
Didier Drogba scored the only goal of the game at Stamford Bridge, firing home at the end of a first half which the Blaugrana had dominated.
Barca had also missed a succession of clear openings during the opening 45 minutes, with Alexis Sanchez striking the bar and Cesc Fabregas miscuing with the goal at his mercy, and proved just as unlucky in the second period, much to Iniesta's frustration.
"We knew that Chelsea always profit from the chances they create," the Spain international told TV3 Catalunya. "They had a few and we weren't good enough to finish ours."
Barca will now have to overturn a one-goal deficit in the second leg at Camp Nou next Tuesday night.
"There's still the return leg to be played and we expect something similar to this one: they will put many men behind the ball," Iniesta said.
"They defend quite well but we will be in our home with our people and that's always a big plus."