Arsenal manager Arsene Wenger blamed some 'unacceptable' defending as Chelsea inflicted a first defeat of the season on the Gunners.
Chelsea went ahead when Fernando Torres was allowed to flick in a Juan Mata free-kick, before another Mata free-kick went in off Laurent Koscielny.
"It is unacceptable to give away goals like that in the big games," said Wenger. "We can only blame ourselves.
"We lacked real authority and decisiveness at the back."
Arsenal had only conceded twice in the Premier League before kick-off but Wenger's decision to leave out Per Mertesacker for the first time and keep Koscielny in alongside fit-again captain Thomas Vermaelen proved decisive.
Koscielny failed to deal with Mata's cross as Torres volleyed in behind him, and then should have cut out Mata's ball in for the winner but could only add a touch to send the ball beyond goalkeeper Vito Mannone.
Wenger said: "I am deeply disappointed. We gave two cheap goals away, they had three shots on goal and scored two goals.
"Was it a mistake to leave out Per Mertesacker? Maybe. But we will never know. We cannot play the game again."
Arsenal rallied after Mata's goal and were only denied an equaliser by two fine saves from Chelsea goalkeeper Petr Cech, who kept out a Lukas Podolski header and a deflected effort from substitute Olivier Giroud.
Giroud then wasted another chance in stoppage time as he skipped around Cech but shot into the side-netting.
"Giroud should have scored," Wenger said.
"He was in a good position to score. Why did he not score? It is hard to identify."