In the first meeting between the two teams in 12 years, Lorenzo Insigne scored for Italy after Gonzalo Higuain and Ever Banega had given Argentina a two-goal cushion.
The young Napoli forward was one of the bright sparks for Prandelli, while Daniele De Rossi also shone filling in at centre-back.
"We met a team of great quality, one of the best in the world," Prandelli told RAI Sport.
"We made mistakes coming out of defence and started badly, but in my view we moved the ball well. We lacked that grit and finishing around the box that a team needs. Credit to Argentina, as they are a very strong side.
"We have to qualify before talking about the World Cup and I want to get there quickly. The experiment with De Rossi, if we want to call it that, went pretty well.
"We all wanted this friendly and I am happy because we saw so many children and families in the stadium. It was not easy to bring 40,000 people to the stadium on August 14, so it means the message was received."
Italy, who currently top World Cup qualifying Group B, still have four matches to go to secure their place at the 2014 tournament in Brazil.
Their next qualifier is against second-placed Bulgaria on September 6.