Dean Huijsen and Evanilson turned the game on its head after Declan Rice had expertly given the Gunners the lead in the 34th minute as the hosts uncharacteristically succumbed to a pair of set-piece routines.
“We started, and we did the more difficult one to score the goal. I think after that we have four or five very open situations to score the second one," said Arteta.
"We didn’t kill it, and after that, you defend the box really poorly when we’ve done it in the two set-pieces that we have conceded again.
“So they’re going to punish you. A team like Bournemouth, they are going to punish you, and after that, the game becomes rash, very chaotic.
"That’s what they want – big spaces. They had more legs than us, especially with certain players that were struggling in the final minutes, and we weren’t able to get the result that we wanted, so very disappointed."
Arsenal have now dropped 21 points from winning positions in the Premier Lague this season, which has played a huge part in Liverpool running away with the title.
Arteta added: “I think every game will probably have a different answer to that. Certainly what happened today is that if you defend the way we did, with very few set-pieces very poorly in the league, you’re going to get punished. It doesn’t matter if you are ahead or behind in the scoreline.
“We certainly wanted to create a really good vibe. A positive result will really help us to build what we wanted towards Wednesday (Champions League semi-final against PSG).
"So what we have created now is a lot of rage, anger, frustration and a bad feeling in the tummy.
“So, make sure we use that for Wednesday to have a massive performance in Paris, win the game and be in the final.”
Bournemouth’s second goal was the subject of a lengthy VAR check after it looked like the ball had struck the arm of the Evanilson, but it was awarded to the frustration of Arteta.
And the Gunners boss was typically coy on the incident, adding: “I have seen a few images, and it looked very different to the decision, but they made that decision.”
The nature of both Bournemouth goals will concern the Arsenal manager, with the Gunners boasting such an impressive record from set-pieces in both boxes throughout the last couple of years.
The result leaves Arteta’s side without a win in their last three matches in all competitions ahead of the Champions League semi-final second leg against PSG on Wednesday.
As they look to overturn a 1-0 deficit from the first leg at the Emirates, their season is at risk of coming to a sudden halt if they are to bow out against the French champions.