The loss is Manchester City's third in a row in one week following a derby defeat to league rivals Manchester United over the weekend sandwiched between their losses against Liverpool in the Champions League. In the first leg, Bayern had won by a score of 2-1, and Real Madrid had scored three unanswered goals.
Roma's victory took the Italians into the European Cup semi-finals for the first time in 34 years.
The La Liga giants travelled to Rome as heavy favourites having comfortably beaten I Giallorossi 4-1 in the first leg.
"So while we compete against Juventus and they've had a great little run, we're kind of all in this together".
Edin Dzeko set the ball rolling in the sixth minute, and after Daniele De Rossi converted a penalty 13 minutes after the break to get the home fans believing, Manolas glanced home a brilliant header with eight minutes left to send the Roma supporters into raptures and leaving Barca wondering what had hit them.
"It's painful because no one expected this after the advantage we had but you realise what the reality of the Champions League is like when you do things badly", a visibly distraught Iniesta told reporters. "The Champions League punishes you for that".
Liverpool weathered a "whirlwind" start from City - as manager Juergen Klopp described it - to advance 5-1 on aggregate.More news: At the Buzzer | Memorable Win Over Cavaliers Vaults Sixers into 3rd Place
"I don't want a side that rests on its laurels or thinks it doesn't matter how the game goes".
The Blaugrana needed to improve in the second half, but instead they conceded a penalty 12 minutes after the restart when Dzeko went to ground under a challenge from Gerard Pique.
His lack of top-level experience showed on Tuesday, though, and the team's European hopes will therefore have to be put on hold for another year at least.
Gabriel Jesus' goal raised belief inside Etihad Stadium that City could do what only two teams had done before tonight and overturn at least a three-goal first-leg deficit in the Champions League knockout stage.
Most of the fans who spoke to Ghanaweb.com said they were "excited about Barcelona's elimination", whiles a group of fans were dumbfounded after they discovered that the Catalans lost to the Romans.
Walter Pandiani, Juan Carlos Valeron and Albert Luque had Depor ahead on away goals before half-time, with Fran Gonzalez - who played for them in the second division in the late 80s and is still their record appearance holder - fittingly scored the fourth to make sure of their passage.