City went into halftime tied 0-0 without conceding any meaningful chances, and they had a decent share of possession. They also did a good job of mixing up their attacks, occasionally slowing down to set up shop in Barca's half and occasionally going all-out on the break. Their defense kept a solid line and the athleticism of Yaya Toure and Fernandinho was tough for Barca to deal with, while the presence of Aleksandar Kolarov on the left wing kept Dani Alves in check. City weren't creating great chances themselves, but they were staying in the game and frustrating Barca. The two teams looked equally likely to score and City looked comfortable.
Only eight minutes into the second half, City's gameplan was destroyed by two back-to-back errors, committed a mere 10 seconds apart. They went from in control to chasing Barca with 10 men, and by the end of the match, they were out of the tie. They have Jesus Navas and Martin Demichelis to blame.
It's generally unfair to pin losses on individuals, but this is a case where an entire team was working well together and executing a gameplan perfectly until one guy screwed up. That guy's error put another guy in a bad position, and that guy proceeded to screw up even worse. All of the hard work done by Toure, Fernandinho, Kolarov and the rest of the City team was instantly undone because two players couldn't block out their regular tendencies that, in this instance, were harmful to their team. City tried to be Bayern, but City can't be Bayern, because Bayern have players who are smarter than Navas and Demichelis.
Navas is a very good winger, but he's flawed in that he only has two speeds: stop and go. Generally, this isn't that much of a problem, since City don't play Xavi and Lionel Messi in the Premier League. When Navas gives the ball away in a league game by running straight into defenders when he should have played a sideways pass to Fernandinho or Toure, it's annoying, but not a death sentence. In this instance, it handed Barcelona their best attack of the game.
Even fewer kind things can be said about Demichelis, who has mostly stunk for about six years, as we noted after Manuel Pellegrini hilariously used him in a two-man center of midfield in a big Premier League match. However, his absurd aggression is occasionally useful and, when he isn't missing wildly with his challenges, he can win the ball back and look pretty good. His lunges aren't always awful, but it's generally a bad idea to go in from behind on Lionel Messi when he gets a step on you. The end result usually looks a lot like this.
Letting Messi go and giving Joe Hart a chance to make a play (okay, let's be real, letting him inevitably clown Joe Hart) would have been a much better decision than hacking at one of the greatest players in the history of the game, but Demichelis' inner monologue is probably something along the lines of 'KILL KILL KILL,' so it wouldn't surprise anyone if he was truly incapable of that.
Pellegrini put together a good gameplan that didn't work out for him because some of his players made bad errors, but it's worth noting that he picked those players in the first place. Even with James Milner, Sergio Aguero and Matija Nastasic out, he had plenty of other options, but he chose a central defender who is demonstrably crazy and a right winger who has problems deciding when to slow down an attack and keep the ball. Right formation, right concepts, wrong players.
While City cleared a big hump in getting out of the group stage for the first time this year, this marks their third straight Champions League campaign that will end in serious disappointment and, ultimately, underachievement. Pellegrini was brought in because Roberto Mancini couldn't get it done in Europe, but he's exiting in the Round of 16, just like he did in his one season as Real Madrid manager. He should get at least one more season as City manager, so time will tell which is the bigger fluke -- his Round of 16 exits or his semifinal run with Villarreal.