Chelsea failed to capitalise on Man City's failure to beat Brighton at home on Saturday and they didn't increase the points gap between them and the City. The Arsenal was simply a better team. Although the game stats look fairly even, it's Arsenal who created much better chances.
As for Man City, they should really push hard and try to do whatever it takes to finish in the top 4 to earn a place in the next season's Champions League. They are awaiting a verdict to their legal battle with the Premier League, when they are charged with 115 instances of rules violation. They will likely end up with big financial penalties as well as possible points deduction, so participation in the Champions League could ease financial losses they might incur.
Both Man City and Chelsea for me are on the same level and Man City had a really good chance that they didnt take against Brighton. They should have won that but this season they are just not on that level as they were. On the other hand it was expected that Chelsea wouldnt do something big,with Palmer out of form its hard for Chelsea to get points