City didn't play at their best, but nonetheless should've been 1-0 up inside two minutes, if it weren't for Sterling's awful finishing. Would've created a totally different game, a much easier one for City to begin with. Same story in the second half, right after the (illegal) 1-0, Sterling should've sealed it but missed another sitter. Sterling's finishing, or lack thereof, is really a big problem and should be worked upon intensively, luckily he's still very young so there's hopes he can improve. One thing's for sure he's not a natural born finisher, so I don't think City or any team will ever get more than 15 goals a season from him.
As for the general level of play, I think City's key players, with the exception of Kompany and Fernandinho, were quite disappointing. Silva had lots of ups and downs. Touré played way too slow. Sterling's finishing, again, was appalling, and so on. As imperious as City look in the Premier League, that's how nervy, shaky they look in the Champions League, overcome by utterly irrational performance anxiety. There's no doubt in my mind that City have more than enough quality to compete with the very best, but the team - the harder they shout the less convinced they actually seem of their own capabilities.
Finally, as much as some City fans hate it, the team is very dependent on Sergio Agüero, with him around confidence automatically goes up a couple of notches and City would effectively have been 1-0 up after just 2 minutes.
And put De Bruyne in the starting XI FFS. The whole idea of buying him was to improve City's chances in Europe, so putting him on the bench won't help that cause.