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.
It is true that it is very unfortunate that Chelsea could not widen their gap with Man City, even though if Chelsea could widen their points gap with City, it would certainly make Chelsea potentially safe and would easily be able to get a ticket to the Champions League. But yes, it is true that Arsenal is still not equal in strength to Chelsea, which ultimately means Chelsea had to accept defeat. But fortunately at that time Man City could not get 3 points because they drew against Brighton, but if only at that time Man City could win against Brighton, Chelsea's position would definitely be shifted and would definitely be replaced by Man City. Man City certainly has to fight hard to be able to reach 4th place in order to get a ticket to the UCL and indeed Man City must start to be able to improve its performance so that it is even better for the upcoming match. Of course, we'll just see what happens later, but what is clear is that it is very unfortunate if Man City does not get a ticket to the UCL.