Ivan Rakitic handed Barcelona the lead in the first half to make it 3-1 on aggregate, and the hosts should have had the tie out of reach far earlier, hitting the post twice before half-time.
But City had a chance to halve the aggregate deficit when Aguero was brought down by Gerard Pique with 11 minutes remaining, only to see his spot kick saved by Marc-Andre ter Stegen.
Joe Hart made 10 saves to keep the score at 1-0, and the result means the Premier League has no team in the quarter-final of the Champions League for the second time in three years.
City, looking to avoid a second straight last-16 exit at the Nou Camp after going out 4-1 on aggregate last season, were on the back foot in the first half, and did not help themselves by picking up four bookings before half-time.
Neymar hit the post in the sixth minute after Vincent Kompany was caught loitering with the ball on the edge of the box, losing possession to Dani Alves before the Brazilian offloaded to his compatriot.
Hart was forced into action in the 12th minute, blocking Lionel Messi???s effort from an angle after Barcelona combined beautifully on the left side of the penalty area.
City???s only half chance of the opening 45 minutes came moments later when Yaya Toure???s centre from the byline was nearly turned in by James Milner, but Alves did well to block the midfielder inside the six-yard box.
But Barcelona took the lead just after half an hour, Messi finding Rakitic at the far post with fine vision for the Croatian to bring the ball down and lob over Hart into the bottom corner.
Luis Suarez hit the post on the stroke of half-time after being put through on goal by Neymar, Kompany and Martin Demichelis drifting apart to allow the former Liverpool striker a run in between them.
Suarez hit the side-netting 20 minutes into the second half, before City failed to get on the other end of Jesus Navas??? cut-back into a dangerous position.
As Barcelona cleared, Neymar found Messi clear on the counter attack, but the Argentine was shepherded out of play by Hart.
City had a chance to get back into the tie in the closing stages when Aguero went down under the challenge of Pique, but the striker???s resulting penalty was saved at a good height to Ter Stegen???s right.
Ter Stegen???s opposite number Hart had to be at his best again to keep out Suarez???s effort after the Uruguayan was played in by Messi.
Hart had to make another two saves in injury time, first from Messi and then Neymar as City left men forward, but the scoreline eventually flattered the Premier League side.