The heavy defeat on Saturday lunchtime ruined manager Arsene Wenger's 1,000th match in charge and severely dented any Barclays Premier League title ambitions, with the Gunners now down in fourth place, albeit still with a match in hand on the leaders.
"We paid for our own mistakes. We have to take it on the chin because it is unacceptable to lose another big game like this," the Spaniard said to Arsenal Media.
"You cannot only just move on, you have to analyse what you have done and react. I am expecting a big reaction on Tuesday (because) Saturday was not good enough for this football club.
"The good thing is we have a lot of things to play for and we have always reacted to disappointments and difficult moments, but this one is a really hard one to take, it was a massive game for us and for me it is unacceptable.
"The pressure we put on ourselves by losing games like that is massive and there is no need for it.
"We just disrupted the good season we were having. I don't know what else to say apart from sorry to everyone at the club, the fans, and we promise that we will try hard to put that right."
Arteta stressed none of the players wanted to produce another shocking display like they did at Stamford Bridge - which had followed on from heavy defeats at both Manchester City and Liverpool earlier in the season.
"It hurts deeply inside. It is embarrassing to be on a football pitch in that situation," he said.
"Psychologically it is really hard, and when you go through that you analyse it and you know you don't want to be in that situation again.
"I promise everyone that we have that hunger to put it right. On Tuesday, we have an opportunity again at home and we just need to bounce back."
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