"It is very painful because nobody expected it with the lead we had," Iniesta told Catalunya TV.
"When you do things badly, you commit lots of mistakes and we didn't adapt to the game. It is a massive disappointment given the season we had been having."
Barcelona went to Rome leading 4-1 after the first leg of their quarter-final tie, but a 3-0 loss at the Stadio Olimpico condemned the five-time European champions to a defeat on away goals.
It is their third consecutive exit from the competition in the last eight. "We always try to give the maximum but we are knocked out and now feel everyone's pain. We had high hopes this season and it has escaped us again," added the 33-year-old, who also acknowledged that the game could have been his last in the competition for Barca amid uncertainty about his future beyond this season.
The defeat came with Barca currently on course to win La Liga and with a Copa del Rey final against Sevilla approaching later this month. They are unbeaten in La Liga and had only previously lost once all season, to Espanyol in the Copa del Rey.
"The dream for all of us was to reach the semis and I'm very sorry to all the Barcelona fans in the world," he told Catalunya TV.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)