Arsenal players have worked hard and they deserved the three points. The match was very tight so it was difficult for both teams to develop the game. But the high tension of the match was very enjoyable and made the match titled London Derby even more different atmosphere. So I congratulate Arteta because he was really able to mix his squad very well even though some of his mainstay players were still unable to be involved in the match.
I don't know what you mean by deserving but the way Arsenal handle the match isn't too nice and well package. Look at the way Tottenham played Arsenal as if they don't used to meet in London Derby only to be playing less of a game. They have less game possessions to than Tottenham and they also have less attempt trying to make th goals, this is why I don't think Arsenal deserve that goal but Tottenham since they are the ones that put everything in that game.
In this Derby, Tottenham looks prepared than Arsenal, it's not like Arsenal weren't prepared but Tottenham had everything on their mind probably because they have won some matched before now while Tottenham is still struggling to balance their game in matches they have next. However, logically one might think that it was because it's away match Arsenal didn't put mouth efferot as they expected.