Seriously Arsenal needs to treat every match as the last match or the deciding match for the league and not lose points. I could remember the year Liverpool won the league with Klopp’s Liverpool team then, he made mention that the way to beat Manchester city is to win just all games and that year he went almost unbeaten before winning it. I think this should be the way arsenal needs to change their perspective to getting the maximum points every game.
Brighton are excellent this season already and didn’t show the momentum’s of a club that has their coach already sacked. They invested in young talents and I think it is gradually paying off this season, if they continue like this they could land themselves an European competitions slot Just like how they did last two seasons.
Arsenal have a very weak perspective when it comes to winning the league and if they had to play against City they feel that by beating Manchester City it will guarantee them the free passage to win the league. Like you said about Klopp, to me is not about winning City but about taking care of your problems then wait for Man City to make their mistakes, that's the thing but Arsenal feels they need to beat Pep's men to win the league and they always forget that the other teams are waiting to strike especially the relegation teams, they too want to stay in the EPL and they need a point at least to survive.
The game against Brighton played much better than when they played against Manchester United, I saw a desperate Arsenal team until the red card came in. The Gunners could not believe how it all happened and I was expecting Brighton to capitalize on that opportunity they had by pressing till they get a goal but they didn't. Even the defense of Arsenal became weak, no confidence in the way the defenders play, that's to show that Rice was very important to the team and if another plan isn't set I believe the Gunners are going to be weak when any important player is shown a red card.