Luis Enrique's men had their hopes of glory in Europe's top competition all but ended in a nightmare last-16 outing in the French capital, as Angel Di Maria struck superbly in each half.
Julian Draxler and top scorer Edinson Cavani also got in on the act and Barca had goalkeeper Marc-Andre ter Stegen to thank for the margin of defeat not being even greater.
No side in Champions League history has come back from such a heavy first-leg deficit but Spain great Iniesta summoned all the defiance he was able to muster when he spoke to reporters afterwards.
"We had a bad day in every way," he said, as quoted by Mundo Deportivo. "In the return we have to try to get as close as possible to turn it around, which is very difficult but we will give everything.
"The word 'attitude' is one I have never liked and I do not think it is linked to these players or this team.
"In the end it is a matter of football. I do not like to talk about attitude when it is not [the reason for defeat].
"It's a game and they have overcome us playing football and taking advantage of all their qualities. We have not been able to in any moment of the match."
Iniesta added: "It is difficult, these things sometimes happen and it hurts. It is a bad night for everyone. It will cost us to take in this defeat.
"We have to get up, turn the page as fast as possible. We have the other competitions, do not forget that.
"When the return comes we will try everything to get closer but it is a tie that is very complicated."