But the Arsenal manager will likely be even happier with the multitude of positives he can take away from a near-perfect evening for the Gunners.
For starters, everyone played well. That seems a fairly obvious statement to make, but often games can be won through strong performances from one or two star individuals.
And while the goalscorers will take much of the credit, it is not exaggeration to claim that every player in the starting line-up and both substitutes that were given enough time to make an impact (Granit Xhaka and Kieran Gibbs) played to an exceptionally high standard.
For a club like Arsenal, this is more crucial than for most. Their expansive, passing play involves more or less every player on the pitch, and for it to really devastate teams, everyone must be on their game, or risk breaking good team moves down.
Arsenal have been long criticised for their approach in big games, but here, it worked to perfection. They weren't naive, but they weren't negative either. They pressed high, but they committed to playing good football, trusted their defensive players and played with freedom. And it worked a treat.
Sanchez was relentless in pressing from the front, and seems to be slowly adapting to the number 9 position. Whether or not it is his best position is still arguable, but it was his best performance in the role to date. He may even have Olivier Giroud worried about his starting spot.
Ozil was inspired, and his link-up play with those around him was almost telepathic at times (not to mention his cheeky no-look pass that bamboozled Nemanja Matic).
Walcott showed all the qualities we knew he could bring to this Arsenal side, while Alex Iwobi proved that he is a genuinely exciting young talent. Quick, calm in possession and with incredible vision, his perfectly-weighted and perfectly-timed through-ball to Hector Bellerin was the key pass in the build-up to Walcott's goal.
But Arsenal were solid defensively too. Shkodran Mustafi was an absolutely immense presence, marshalling Diego Costa in a physical but level-headed manner that the Gunners have failed to produce against the centre-forward all too often.
In addition, Bellerin demonstrated why he had been so keenly sought-after over the summer. He made up for the one defensive mistake that was made when Laurent Koscielny allowed Pedro to pick his pocket, racing back with unbelievable pace to deny a clear goal-scoring opportunity and preserve their clean sheet.
Francis Coquelin's injury was maybe a lone negative on an otherwise perfect evening, but even that showcased the strength in depth that Arsenal possess, able to comfortably replace a player and not see a dip in quality.
Perhaps most important for Arsenal was to break their psychological barrier against a team that has often caused them trouble, and to have broken it playing the way they want to play.
If they continue in this vein, they will be the force that they have been expected to be for many years. Whether they actually go on like this remains to be seen.
Have something to tell us about this article?