The Premier League leaders were stunned 2-1 by the Cherries, so leaving Arsenal nine points ahead of Manchester City - but having played two games more.
Asked about his pre-match plea to fans to rally around the players, Arteta said: "Apologise, take it on the chin, and that's it. What I'm trying to do is give our best to the club, give the responsibility to our players.
"And I know if the atmosphere, the fans, the support, the energy in the stadium is the best in the world. We have a much better chance. I don't think that there's any other possibility to perform better than when you have that kind of support. But then we have to respond.
"And we had moments in the first half where we did it and there were other moments that we were on our level. So, yeah, we have to apologise to them and improve."
Arteta also sought to lift his players, admitting he can see title nerves beginning to have an influence.
"We have to embrace it and especially enjoy the opportunity," he said. "That's one of the things that I haven't seen the team today. That level of enjoyment in certain moments. That's a fight that we have to have to really change the course of the game when it goes difficult.
"We're going to have different contexts from here to June. And we need to be able to adapt and resolve all of them. If we want to achieve what we want to achieve."