It was as good as over the moment that Laurent Koscielny fixed his grip around the torso of Edin Dzeko in the 11th minute and redoubled his efforts to haul the Manchester City striker to the ground. The home crowd at the Emirates knew defeat was coming; it was just a question of when the bad news would be delivered.

This was a snapshot of the modern Arsenal. Incompetent in defence, resolute when the chance of victory had already passed them by and ultimately too lightweight to get a victory against one of the big boys of the Premier League.

As he left the pitch at the end of the game, Gaël Clichy was jeered by a group of Arsenal fans around the tunnel and responded by pointing to the Premier League winners’ badge on his sleeve. It was brief and to the point. City left town with their own grievances about the referee Mike Dean but they did the job as befitting a team who are staying doggedly on the trail of Manchester United.

Like all good sides, they identified the vulnerabilities in this Arsenal team and did not allow them to retreat behind the ball and hold out for the draw which would have been a decent result for the home side after Koscielny’s dismissal.

The reaction afterwards from Arsenal manager Arsène Wenger was telling. He barely lingered on the Dean decision to dismiss Koscielny instead airing the kind of criticisms for his side that he presumably usually keeps private. He accused them of being “timid” and lacking “authority”.

“We are a bit too nervous to play in a serene way,” Wenger said. But serenity is the preserve of the truly great; Arsenal would be best served starting with some rigour and discipline and working their way up from there.

Instead, they were down to 10 men within 11 minutes against the defending champions. It was a crazy challenge from Koscielny, borne of a panic that is inadequate in these kind of high-pressure situations. He wrapped his arms around Dzeko and heaved him to the ground. The City striker was in on goal, it was a denial of a goalscoring opportunity and for Arsenal it was a denial of a three-point opportunity.

Even when Dzeko had his penalty saved – off Wojciech Szczesny’s legs, against the post and back into the goalkeeper’s arms – there was still very little doubt that City would win this game.

Wenger complained that his team did not impose their “personality” on this match but what is the Arsenal personality these days? Occasionally dazzling in attack, often profligate in defence, they might best be described as schizophrenic with, on occasions such as this, bouts of depression.

The Premier League table now has Arsenal in sixth place, 21 points behind leaders United and 14 off City in second place. They have played one game fewer than the entire top half of the table, Chelsea excepted, and if they win their match in hand they will be only three points behind Spurs in fourth. But they only started playing yesterday in the second half when hope was all but extinguished.

As for City, they keep United just about in sight. Roberto Mancini said after the game that if they could be within five points of their neighbours come the derby at Old Trafford on 6 April then the title was still a possibility and it was performances such as the one from the first goalscorer James Milner that caught the eye yesterday.

On 21 minutes, Lukas Podolski clipped the heels of Javi Garcia in midfield. Gareth Barry played the free-kick out right to David Silva, from there it went on to Carlos Tevez and then Milner while Arsenal’s defence were still strolling back. The England international whipped a shot across goal and past Szczesny before Arsenal’s back four had stirred, and from there the game was heading in one direction only.

The second from Dzeko came after the half-hour. Milner drove in from the right and Tevez reacted first to get a touch on his cross, allowing Dzeko to tidy up at the back post. City are unbeaten in three league games since the defeat to Sunderland on Boxing Day, only one of two league defeats all season. It would have been an ideal day for City were it not for Vincent Kompany’s red card.

Mancini said that he would appeal against the decision – delivered by Dean when Kompany went in on Jack Wilshere on 74 minutes – and the City manager was confident that the decision would be overturned. It was a close call but the studs were raised, both feet were off the ground and Dean was entitled to decide under the current law that Kompany was reckless and out of control. It is irrelevant how many ex-professionals claim that the “game has gone” because such tackles are now outlawed.

Wenger identified a shot from Theo Walcott, that was cleared off the line by Joleon Lescott, and a slack header from substitute Olivier Giroud, which went over the bar, as moments when his side should have done better. He has also lost Mikel Arteta, absent yesterday, to injury for the next “two to three weeks” – a serious blow especially considering Arsenal play at Chelsea next Sunday.

The Arsenal manager did not give much hope that reinforcements will be found this month. “To find a player of Arteta’s calibre in January – good luck with that” was his view of the current market. The trouble as ever is that no one is good enough for Wenger but then neither, on this evidence, are his current squad of players. You would assume that something has to give, but this being Arsenal, the chances are it probably will not.

Match facts

Arsenal: SZCZESNY 6/10, KOSCIELNY n/a, SAGNA 5, VERMAELEN 5, GIBBS 5, OXLADE-CHAMBERLAIN n/a, DIABY 5, CAZORLA 5, WILSHERE 6, PODOLSKI 5, WALCOTT 5

Manchester City: HART 6, CLICHY 6, NASTASIC 6, KOMPANY 5, ZABALETA 7, SILVA 6, BARRY 7, TEVEZ 6, GARCIA 6, MILNER 7, DZEKO 7

Substitutes: Arsenal Mertesacker 6 (Oxlade-Chamberlain, 12), Giroud 4 (Podolski, 56), Ramsey 5 (Diaby, 62).

Manchester City Lescott (Tevez, 76), Balotelli (Dzeko, 88), Kolarov (Silva, 90).

Booked: Arsenal Vermaelen, Wilshere. Manchester City Milner, Clichy, Garcia, Barry.

Sent-off: Arsenal Koscielny (10). Man C Kompany (75).

Man of the match Milner. Match rating 6/10.

Possession: Arsenal 45%. Manchester City 55%.

Attempts on target: Arsenal 4. Manchester City 9.

Referee M Dean (Wirral). Attendance 60,107.