(Cesar Azpilicueta 25, Juan Mata 66)
It was only the League Cup, it was only a skirmish between two weakened sides.
Arsenal fans can tell themselves that, if they think it will help.
The nagging truth, however, is that anyone looking for evidence of Arsenal's title credentials will have found little to satisfy them at the Emirates Stadium on Wednesday morning (Singapore time).
There is no question that Arsenal have a first 11 that can match anyone in the Premier League. The problem is what lies beneath.
In a battle of the fringe players, Arsenal's spare parts came a very distant second.
Even the late introduction of Mesut Oezil and Olivier Giroud had little effect. By that time, the game was already lost.
Much has been made of the return of Nicklas Bendtner, hasty conclusions derived from fleeting appearances from the bench.
Under deeper scrutiny, played from the start, the not-so-great Dane fell short again.
Carl Jenkinson, understudy to Bacary Sagna, was responsible for the first goal, carelessly dropping a header short of his goalkeeper and allowing Cesar Azpilicueta to open the scoring.
Jenkinson is a lifelong Arsenal fan whose commitment can never be questioned, but it remains to be seen if he is of the necessary calibre.
The signing of Oezil was quite obviously a success, both on and off the pitch, but it should not have been the end of Arsenal's spending.
There is no back-up for Mathieu Flamini and, given this performance, there is precious little to support Giroud. It would not take a genius to predict the contents of Arsene Wenger's Christmas shopping list.
If the board really wants to compete with the likes of Chelsea and Manchester City, they need to match them with numbers as well as quality.
Arsenal were too narrow and failed to stretch Chelsea in the way that they have stretched so many other teams this season.
There was barely any link between the midfield and the lone attacker.
It was a flat, spiritless performance and that will have stuck in the craw of so many in the stadium.
League Cup or not, this was still Chelsea and they expected better.
The 9,000 Chelsea supporters, on the other hand, had the time of their lives.
They baited the home supporters throughout, singing songs about European Cups and titles, mocking the Gunners for their trophy drought.
This was also, lest we forget, another opportunity to end that drought.
Chelsea, by virtue of their strong, disciplined squad, now find themselves in the last eight.
Given Mourinho's record at Stamford Bridge and the two-legged semi-finals, it's not hard to see Chelsea at Wembley in February.
This was the first competition that Jose Mourinho won at Chelsea.
He has spoken in the past of its importance to cultivating a winning culture. How they would love to have a winning culture at Arsenal.
Regardless of the importance of this competition, games like this can be crucial in building morale and momentum.
Those attributes now belong exclusively to Chelsea. Juan Mata's glorious goal in the second half would put the spring in anyone's step.
This is by no means a disaster, even if it is the second defeat in three games.
Arsenal are still at the top of the Premiership table and will still be a formidable force. But you wonder what will happen if they lose Oezil to injury.
You wonder how they will cope when the games begin to catch up on Giroud.
They have already lost Flamini and they miss him terribly.
Arsenal are an excellent team, but Chelsea have an excellent squad.
After this game, there's only one team that you would feel comfortable backing for the title.
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