Mikel Arteta said his Arsenal team took total blame for their late defeat at Brighton and that improving their concentration was "non-negotiable".
The Gunners' miserable restart continued with an injury-time winner from Neal Maupay earning Brighton three points and sealing back-to-back defeats for Arteta for the first time as Arsenal head coach, and give Brighton their first league win of 2020.
Nicolas Pepe's goal looked likely to return Arsenal to winning ways following their 3-0 reverse at Manchester City in midweek, but a poorly defended corner allowed Lewis Dunk to bundle in from close-range before Maupay struck in the fifth minute of added time - with goalkeeper Bernd Leno earlier stretchered off to compound the Gunners' day.
"I think we did a lot of things to win the game comfortably, but we haven't competed like you have to in the Premier League, to give the first goal like we did away and lose a few duels afterwards, it's all our fault," Arteta said after the game.
"I'm not concerned about our character, but how we compete in a Premier League match. It's 100 minutes in this case, every ball, every action. The moment you lose concentration the opponent is going to punish you, it's not the first time it's happened, and if you want to win matches consistently at this level that's a must - it's non-negotiable.
"I think we competed for a large part of the game, but in crucial moments when you don't, you pay the price. It's my fault as I'm the one who has to make sure they do."
Arteta responds to Maupay criticism
Maupay had cut a controversial figure throughout the game after being involved in the clash which saw Leno stretchered off before half-time.
The German goalkeeper had directed his anger at the forward as he was led from the field, while Maupay was later confronted by a number of Arsenal players at full-time in an incident which began with Matteo Guendouzi appearing to strike him.
Arteta said there had been no update on the scale of Leno's injury but took issue with Maupay's claims in his own post-match press conference that Arsenal players lacked humility.
"I think no player has the intention to hurt anyone, I think it's the same here, it's unfortunate," he said. Bernd's injury doesn't look good, it can happen, we'll analyse it tomorrow. We think he had a hyperextension of the knee and we'll have to assess the damage.
"I haven't seen the action [at the end of the game], I've seen a lot of players just talking about getting together, but I didn't know what happened.
"It's the frustration because we threw the game away, and that's a reaction that can happen. I always believe that a player has no intention to get someone else injured. He can say whatever he wants, I know my players and I know one thing they don't lack is humility."