A disappointing draw against the Republic of Ireland was followed by the stalemate against Luxembourg, as Maxime Chanot netted with five minutes left for the minnows.
Italy were denied by the woodwork twice but failed to show their best form and are now without a win in seven matches.
Chiellini told Sky Sport Italia: "I am sorry about the result.
"I can promise you that we wanted to do well. During the past few years we haven't proved to be great at friendlies, but fortunately we seem to be okay when it gets serious.
"We have to move forward with confidence and make sure we're ready for the England game in 10 days' time."
Midfielder Marco Verratti is confident Italy will be at their best against England when they kick off their World Cup campaign in Manaus on June 14.
"This was the first game in which we tried a new plan," Verratti told RAI Sport.
"It's unthinkable that we'd be at our best already. We're working hard, but we know that when the World Cup comes around we'll be ready.
"The result wasn't what was important today."
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