The 33-year-old, whose Italy side face Germany in Thursday's semi-final, has never been a regular scorer from his deep-lying midfield role but wowed the tournament with his chipped penalty in the last-eight shootout win over England.
Asked if he thought he deserved to be named the World Player of the Year having also guided new side Juventus to the Serie A title in May, the 2006 World Cup winner was categoric.
"No, there is (Lionel) Messi and (Cristiano) Ronaldo. It's almost impossible to be in front of them," he told a news conference that included journalists from as far afield as the United States and China.
"They score lots of goals. I don't think it is under discussion."
Whatever modest Pirlo says, creative players like him are generally outshining strikers at the tournament and the Italy man warned his team mates of the threat posed by another midfielder in good form - Mesut Ozil.
"There are lots of good Germany players but Ozil is crucial for their game," he said, fearing the extra preparation time Germany and Ozil have had for the Warsaw clash could be a factor.
"Two days less is a lot in an important phase of a championship. It would have been better to have it more balanced."
Nevertheless, Pirlo thinks Italy will trouble Joachim Loew's side, who have never beaten the Azzurri in a World Cup or Euros and lost to them in the 2006 semi-final on home soil.
"Germany for sure will be scared of us," he said, reckoning the Italy midfield is "more or less at the same level" as Spain's engine room.
"I'm curious to play in this important game. I'm almost at the end of my career and these emotions might not happen again."