Arsenal spent 248 days at the top of the Premier League table this season but still lost out to Pep Guardiola's side for the ultimate prize.
A 1-0 defeat at Nottingham Forest over the weekend ensured City were crowned champions of England for a third straight season.
While City have embarked on a remarkable 12-game winning run at the business stage of the season, Arsenal won just two of their last eight matches to take runners up spot.
Arsenal's title drought has now stretched to 19 years and Arteta knows his side have so much more to do to match the champions.
“This is my job, this is our job, and this is what this club deserves,” Arteta said after the loss to Forest.
“It wasn’t enough. I know we’re not at that level, but we have to find a way. This is not enough. It’s not going to change in three months time. We need to be at that level but we need to find other ways to do it.
“For example at Forest we needed to play much better. This is my responsibility.
“That’s why we have to push for that to happen. That’s not going to happen if we don’t make a lot of right decisions and think smart and have the mentality every day to get to that level.”
Arsenal's consolation for missing out on the title is a return to the Champions League for the first time since the 2016/2017 season.
