The stand-in captain has also vowed they will get things right when Swansea come to the Emirates Stadium on Tuesday night.
The heavy defeat on Saturday lunchtime ruined manager Arsene Wenger's 1,000th match in charge and severely dented any Barclays Premier Legue title ambitions, with the Gunners now down in fourth place, albeit still with a match in hand on the leaders.
Wenger - who cancelled Monday morning's scheduled pre-match press conference - has been left puzzled by his side once again failing to turn up in a big game; Arsenal found themselves 3-0 down by 17 minutes, and played out the rest of the match with 10 men following the sending-off of defender Kieran Gibbs in a case of mistaken identity, which is expected to be overturned by the Football Association.
Arteta accepts the Gunners were "just not good enough" and have no option but to raise performance levels against the Swans, with the squad having held a debrief session at their London Colney training base on Sunday.
"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."
Arsenal are hoping defender Laurent Koscielny will shake off a calf problem which saw him replaced at half-time to be fit to play on Tuesday.
The club are also understood to be set to appeal against Gibbs' dismissal by referee Andre Marriner, for which the official quickly apologised on Saturday after the match.
The suspension would instead be transferred to Alex Oxlade-Chamberlain, who had committed the handball and indeed admitted his guilt at the time but was waved away.
However, Arsenal may then also move to have that red card downgraded, claiming the midfielder had not in fact technically prevented a clear goalscoring opportunity as the shot from Chelsea's Eden Hazard looked to be going just wide.
Wenger later confirmed on the club's official website, www.arsenal.com, that defender Koscielny would miss out on Tuesday night.
Captain Thomas Vermaelen is likely to play at centre-half alongside Per Mertesacker, while 19-year-old Spaniard Hector Bellerin, who was on loan at Watford, has been drafted into the squad as cover.
"We have lost Laurent Koscielny for Tuesday's game with a calf problem. I don't know how long he will be out for. He has a scan today [Monday]. Everyone else should be available," Wenger said.
The Gunners boss was also hopeful of having both Gibbs and Oxlade-Chamberlain available against Swansea.
"There is a question mark about Chamberlain. The situation over his suspension will be decided today. After that I will make a decision. At the moment he is in the squad. We expected Kieran Gibbs' suspension to be overturned," Wenger said.