Manchester City and Real Madrid always give a lot of importance to their domestic league and Champions League but we don't see that in case of Arsenal. Arsenal may take the English Premier League tournament very seriously but they are not too interested in the Champions League tournament. If they had given more importance to the Champions League tournament, their performances in the Champions League would not have been so bad on a regular basis, while in the English Premier League they are rightly second in the points table.
Arsenal are just beginning to pick form in the premier league as they weren't title contender before but for the last two seasons, they have been the only one chasing Manchester city. I think Arsenal wants to win the premier league first before they start concentrating on the champions league as it would be much easier to win the premier league than to win the championship league. The champions league has alot of heavyweight clubs that arsenal can't comfortably win. There's Real Madrid, Bayern Munich, Manchester city and Liverpool is right there above them when it comes to champions league therefore winning the premier league should be their priority first.