The Blues led on two occasions throughout the contest before the Gunners got their noses in front at 3-2 early in the second half.
Juan Mata leveled it up with nine minutes remaining before missing a good chance to put the home side ahead and Villas-Boas rued that miss as it went a long way to contributing to the defeat even though Chelsea were poor defensively.
"The decisive moment might have been when Mata was free on goal and misses the chance to go 4-3 ahead," Villas-Boas told Sky Sports 2.
"We've seen some great open games recently between the top teams and this is one more. We will have to reflect on the mistakes we made and there are a couple of things we can improve, but the commitment and desire is there.
"We must evolve, it's a loss against a big team picking up form, it's two defeats in a row and we have to get things right."