The 2006 World Cup winner was not picked by Italy chief coach Antonio Conte even though the likes of Riccardo Montolivo, Claudio Marchisio and Marco Verratti were ruled out by injury.
The United States league is not considered to be competitive enough to get him a place in the national set-up.
"The moment I decided to go to New York, automatically it was clear with Antonio Conte: 'If you need me, then I'm here, but if you call someone else then I understand'," Pirlo was quoted as saying by La Gazzetta dello Sport on Sunday.
"Not seeing me as often as the others, Conte couldn't know my condition as well as them. So he called others. Italy don't miss me. I think I did what I had to with the Italy shirt."
The 37-year-old also said he is sure Italy would do better without him at the competition. One of the best midfielders of the game and known for his vision and long passing, Pirlo has represented Italy in 116 games.
"I do miss the Nazionale, but I knew that I would. Even just sitting in front of the TV, you feel the adrenaline and realise how much it affects you. I don't think Italy need me, as they are doing very well and will do even better, you'll see."
Speaking about 23-year-old Verratti who was ruled out with a sports hernia, Pirlo said that the 23-year-old's game is similar to his. Paris Saint-Germain player Verratti has been groomed to replace Pirlo in the deep-lying playmaker role.
"Perhaps he is the player that most resembles me. He certainly would've been one of the stars of this Euros and he will definitely be the leader of Italy in future. He has everything required for that role," he reckoned.
"In Europe I don't really see players who are like me. Maybe that's fortunate, as I'd be a bit sad Of course I would've liked to be called up and play for the Nazionale, but in my mind it was far more of an 'I'd like that' as opposed to 'it'd be the right thing to do"."