Barca held a three-goal advantage going into the second-leg at the Stadio Olimpico last night, after beating the Serie A side 4-1 at the Camp Nou last week.
However, Eusebio Di Francesco's side provided their home fans with an unthinkable result to eliminate one of the overwhelming favourites for the title.
And Iniesta, who looks likely to depart to China at the end of the season admits it's been a bitter pill to swallow - considering it may be his last game in Europe's elite club competition.
"That is a possibility and for that reason, it hurts even more," the veteran playmaker told Marca. "It's a very hurtful elimination because nobody expected it due to the lead we had.
"When you do things badly, make lots of mistakes and don't adapt to the game, this is what happens.
"It's a big disappointment because of the season we were having. It's difficult to take this elimination because we had a lot of hope and it has escaped."