The referee decided the match in the 9th minute. Koscielny let Dzeko get behind him, put his arms on him, and Dzecko collapsed to his knees as if a gorilla had landed on his back. Judged to be the last man preventing a goal-scoring opportunity, even though Man City still got a decent shot away, Mike Dean awarded a penalty and sent off Koscielny with a red card. Game over.
Szczesy actually saved Dzeko's penalty shot, with an assist from the far post which rebounded the ball back into the goalie's arms. But Arsenal were down to 10 men against one of the best teams in the world. Yes, they were at home. Yes, they had the depth to bring on Per Mertesacker to replace Koscielny in the center of defense (requiring the sacrifice of Alex Oxlade-Chamberlain on offense).
Clearly affected by the combination of bad luck, poor defense, and dubious officiating, Arsenal were all over the place for the next 20 minutes of the first half, ceding virtually all of the possession to Man City. In the 23d minute, City pressed home their advantage, when Milner scored on a terrific shot, after Vermaelen failed to track his run into the box. Ten minutes later, Dzeko made up (sort of) for his penalty miss with a tap in, after Szeszny had done well to parry a late deflection by Tevez. The ball went straight to the unmarked Dzeko, who could not possibly have missed from one yard out.
After that, there seemed not way back for the under-manned Gunners (especially given their willingness to allow the usually errant Theo Walcott to take free kicks in the third). Out shot 12-2 in the first half, it remained to be seen what kind of reorganization Arsene Wenger could possibly pull off at half time that could make any difference.
In the second half, Arsenal played with great heart. And Mike Dean pretended to even things up by issuing an equally dubious red card to Vincent Company for a supposed two-footed tackle, after Company had clearly won the ball. But it was too little, too late. Arsenal created a few chances, and really should have scored when substitute Olivier Giroud had an open header five feet from the goal. But the combination of Manchester City and Mike Dean were simply too much of an obstacle to overcome.
Man of the match: Referee Mike Dean. He completely dominated the match and determined its outcome, issuing two red cards and six yellows. If the best refereed game is one in which the referee is hardly noticed and makes no controversial decisions; this was one of the worst refereed games ever witnessed. The FA ought to show Mike Dean a red card, sit him out for a few games, and make him review the rule book as well as videos of well-refereed games.
Just one other thing: Jack Wilshire has enormous heart. He was nearly kicked off the park by Man City (according to one report I read he suffered more fouls today than any player in the league has all summer); and he did a fair amount of kicking of his own. He represents the best of the past and the future of Arsenal Football Club.