The Blues took a first-half lead when Juan Mata capitalised on Paolo Cannavaro’s mistake and produced a composed finish past Morgan De Sanctis.
However, the Serie A outfit responded, with goals from Ezequiel Lavezzi and Edinson Cavani putting the home side back in front before half-time.
And Lavezzi struck again in the 65th minute to land a severe blow to Chelsea’s hopes of winning the quarter-finals.
“After the first goal we had the chance to go 2-0 up but missed some big opportunities,” said Villas-Boas.
“We should have done better defensively. We made a couple of mistakes that against Napoli, with their attacking strength, you will get punished.
“The third goal was perfectly avoidable. If they only had a one-goal advantage to take to Stamford Bridge it would have been better.”
Napoli made a bright start, and the home supporters were left stunned when Mata nicked in past Cannavaro to hand Chelsea a surprise lead.
But the Blues failed to take advantage of their good fortune and Lavezzi punished Chelsea for lacklustre defending, as the Argentine forward unleashed a curling shot past Petr Cech from 25-yards out.
Then, on the stroke of half-time, Cavani turned home Gokhan Inler’s dangerous cross to hand the home side the lead.
Chelsea improved in the second half but were unable to score a second away goal, and David Luiz was punished for a sloppy defending when his clearance deflected into the path of Cavani, who teed up Lavezzi to score Napoli’s third.
With Chelsea’s prospects of reaching the quarter-finals in the balance, Ashley Cole cleared Christian Maggio’s late effort off the line after excellent work from Marek Hamsik.
Despite the defeat, Villas-Boas remained upbeat about Chelsea’s prospects of overturning the Italian side’s first-leg lead in three weeks’ time at Stamford Bridge.
“It is more difficult to recover now but not impossible of course because of the amount of chances we created and the environment, which we must create at the Bridge to turn this tie around and go through,” added the Chelsea boss.
ENHANCED ODDS: Get 7/1 on Djokovic to win the US Open