Arsene Wenger's 1,000th game as Arsenal boss quickly turned sour as the visitors to Stamford Bridge conceded four goals before half-time en route to a humbling loss.
The result represented a damaging blow to Arsenal's hopes of landing the Premier League title, and followed heavy reverses earlier in the season at the hands of Manchester City and Liverpool.
Arteta has promised he and his team-mates will give their all to put things right in the matches that remain this season.
"It's not good enough with the way we started the game," he told the club's official website.
"We paid for our own mistakes. We have to take it on the chin because it's unacceptable to lose another big game like this.
"The pressure we put on ourselves by losing games like that is massive and there's 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.
"It hurts deeply inside. It's embarrassing to be on a football pitch in that situation."
Arsenal, who now trail Chelsea by seven points but have one game in hand on Jose Mourinho's men, will seek to bounce back when Swansea City visit the Emirates Stadium on Tuesday.
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