When this narrow scoreline is inscribed in the Champions League history books, it needs to be accompanied by an asterisk denoting the influence of Joe Hart.
Manchester City are out of Europe and were lucky it was not a rout. Only the greatest performance of Hart's career rescued City from an almighty mauling.
There can be no consolation from another departure from Europe, and the inquest will deepen for Manuel Pellegrini, but there had to be huge admiration for City's remarkable keeper. Having saved a penalty from Lionel Messi in the first leg, Hart proceeded to deny Messi again, Luis Suarez and particularly Neymar. Hart made seven superb saves and had no chance with Ivan Rakitic's first-half goal, his defence and midfield -having left him exposed as Messi dominated. Within five minutes, Pellegrini had risen from his seat, standing at the edge of the technical area, gesturing his team to push up as they started to be pummelled by Neymar, Luis -Suarez and, particularly, inevitably, mesmerisingly, Messi, that elegant nemesis of so many of Barcelona's opponents.
The half-time statistics revealed Messi had touched the ball 56 times, had three efforts on goal, and one assist. Even before he created Rakitic's first-half goal, leaving City 3-1 in aggregate arrears, Messi was twisting Aleksandar Kolarov, Fernandinho and company into tiny sky-blue knots.
Up in the Gods, where the oxygen was thin, and the confidence thinner, City's 4,000 fans peered down, straining to pick out the human ants speeding around below. At least it was easy to spot Messi; he tended to be the one with the ball. However distant, Barcelona's threat was clear.
Mistakes were seized on.
The pain began early. When Vincent Kompany dawdled on the edge of City's box, Dani Alves nicked the ball and swiftly released Neymar. The Brazilian struck the ball low and hard, and turned away, beginning to celebrate. He was so convinced his shot had beaten Joe Hart. It had but it clipped the post, bounced across in front of the goal, and eventually span away to safety. Pep Guardiola, making his first return to the Nou Camp since he resigned three years ago, was out of his seat, his celebration short-lived.
Yet much of the magic he nurtured was seen. Guardiola enjoyed the prodigious services of Messi, and will have watched the little genius admiringly, along with the rest of the Barcelona fans, and doubtless, however grudgingly, the City supporters. Messi was, again, bewitching. If there was an award for European Golden Nutmeg, Messi could have declared at half-time. Fernandinho, then James Milner suffered the indignity, although some would say the honour, of having Messi guide the ball between their legs, and running on.
As the Barcelona supporters chorused "Messi, Messi", the Argentine almost scored a wonderful first-half goal following a move of quickfire return passes.
He passed to Neymar, and received the ball back. He passed in to Andres Iniesta, and collected the return, being denied brilliantly by Hart.
City had rare excursions out of their half. Yaya Toure cut the ball back to Milner, whose shot Alves blocked. Kolarov had a shot held by Marc-Andre ter Stegen. Sergio Aguero, a frequently isolated front-runner, had a shot intercepted by Gerard Pique.
Normal service was always resumed, normal Barcelona possession, pushing deep into City territory. As he looked on helplessly, Pellegrini's side were creaking, their indiscipline surfacing, bringing bookings from Gianluca Rocchi, and conceding so many free-kicks that the Italian referee risked running out of vanishing spray. Fernandinho was cautioned for fouling Neymar, gifting Messi a free-kick which he swept just over to a mass "oooh". Kolarov then body-checked Messi on the touchline, the offence bordering on -violence. Another booking.
Messi would not be quelled. He responded to City's rough tactics by nutmegging Fernandinho. Messi was then fouled by David Silva, of all people. Messi almost deepened the punishment with another free-kick.
For all his individual gifts, Messi is also a team player, constantly looking to send team-mates through. After 31 minutes, Barcelona's No?10 bamboozled Milner and Kolarov before lifting a great pass over City's retreating backline. City had been drawn across, Bacary Sagna going with Neymar, leaving tempting space towards the far-post. None of City's midfielders had tracked Rakitic, who ran in and lifted the ball over Hart for his first Champions League goal. Messi's face was a picture of pure joy as he ran in to congratulate Rakitic.
The fouls continued. Toure kicked Suarez. Samir Nasri hacked at Neymar. The chances continued. Suarez struck the post. City's goalkeeper was working overtime. The second half brought no respite. Hart did well to keep out an effort from Iniesta, and then, athletically, punching clear a shot from Messi.
Pellegrini had withdrawn Nasri at the break, sending on Jesus Navas down the right. Milner assumed a more central station, allowing Toure to push on. He had been too deep to have any influence in the first half.
City played better in the second half, and there was a real moment of hope in a goalmouth scramble when Navas, Milner and Kolarov went close, but were still vulnerable to the counter. Suarez hit the side-netting from one breakaway. Then Messi was sent racing through by Neymar, but he failed to beat the outstanding Hart. England's No?1 then slid in clear from under the feet of Messi, a manoeuvre that demanded perfect timing
At times it felt that Hart was facing Barcelona on his own. He saved from Neymar and then rushed out to defy the Brazilian again, this time with his feet. It was a magnificent performance by Hart, and one that kept City just about alive. Wilfried Bony had replaced Toure, who received a warm salute from his old supporters. Bony soon linked well with Aguero but sent his shot into the stands.
City's hopes were fading and disappeared when Aguero missed a chance to score from the spot after 77 minutes. Aguero had won the penalty, running into the box, and taking evasive action when challenged by Pique with Javier Mascherano close by. Barcelona were unimpressed, giving their celebrations an extra intensity when Aguero placed his penalty too close to Ter Stegen. As the Barcelona players surrounded their German keeper, congratulating, it was very noticeable that none of the City team rushed to console Aguero.
Down the other end, Hart continue to perform miracles, denying Neymar in another one-on-one, and somehow repelling a close-range shot from Messi.
Frank Lampard came on to respectful applause from the Barcelona fans. By this point, the locals were admiring Hart's expertise. Again Neymar ran through, this time released by Pique. Again, Hart stood firm.
Suarez tried his luck to no avail and responded, sportingly, by embracing Hart. At the final whistle, Suarez was first to salute Hart. City's keeper was last off the pitch at the end. His team were out but Hart could leave with his head held high.