Italy suffered a 2-1 loss to Argentina at Rome's Stadio Olimpico - the first match between these two countries in 12 years - as Napoli new boy Gonzalo Higuain fired a warning shot to Serie A defenders everywhere by scoring one and making another in a one-sided friendly.
Lorenzo Insigne lofted an effort over Mariano Andujar with 13 minutes left to renew home hopes but Argentina finished stronger.
Chiellini told reporters: "Argentina have some really good players in attack. We worked hard, but we probably paid the price for starting pre-season later than many of them.
"It was clear out there - we were always second to the ball and we were not able to stay as compact as we would have wanted.
"We wanted to beat Argentina because it is important to do so in games like this."