Barcelona struggled under a barrage of crosses and set-pieces, with first-leg own-goal villains Daniele De Rossi and Kostas Manolas completing the job from a penalty and a corner respectively.
"It's a very hurtful elimination because nobody expected it due to the lead we had".
"We came from a very positive dynamic this season and today, sadly, everything has been cut short".
Barcelona star man Lionel Messi has blamed his team's Champions League exit on want away defender Samuel Umtiti.
"The main error we could make is thinking we're in the semis already", added Valverde, who took exception to the tone of questions he felt suggested Barca progress is a formality.
Iniesta has won four Champions League titles with Barcelona is an iconic player for the Catalan side and if he is to leave Barca and bid goodbye to the Champions League then it could be considered a awful blow for football as well, particularly given the way that this midfield maestro has dominated the European football scene with his football.
'We looked at the game in the first leg... we've watched Barcelona for a number of months now and I'm not sure - even though they haven't conceded many - I'm not sure you cannot concede when you've got two strikers that don't put anything into defending.
"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", Iniesta said.
Manchester City's Sergio Aguero shows his disappointment. Although a different competition, Roma didn't have the ideal preparation for this fixture by losing at home to Fiorentina in Serie A.
A dejected Pep Guardiola is seen in the stands after he had been sent off the pitch.
Manchester City's Leroy Sane is tackled by Liverpool's Dejan Lovren.