Barca travelled to the Parc des Princes for their UEFA Champions League Group F clash having won six of their seven competitive outings without conceding a goal this season.
However, strikes from David Luiz, Marco Verratti and Blaise Matuidi condemned the Spanish giants to a first loss under new coach Luis Enrique, as goals from Lionel Messi and Neymar were not enough for them to take anything from an enthralling contest in the French capital.
And, speaking after the game, Iniesta rued lapses made by Barca, but also remained upbeat about their prospects of recovering from the setback.
"In some phases, they were the better side," explained the 30-year-old.
"You pay dearly for mistakes in the Champions League, when your opponents take their goal chances.
"We reacted quickly after they scored, but we found it hard to equalise or turn the game around.
"It's tough not to win but we have to keep going. It's not easy to play here in the Champions League, but we need to carry on as we have done until now.
"Nobody gives anything away for free - we lost but we just have to press on."
Javier Mascherano agreed with Iniesta's comments, saying "you pay a high price for slight errors in games like this".
"Defeats are always worrying, we need to improve," added the Argentina midfielder.
"We have to lift our heads because this hasn't finished yet. We need to correct our mistakes and keep improving."
