The Sunderland-owned forward was full of praise for coach Antonio Conte, who he says prepared his team down to the smallest details to beat the two-time defending European champions.
Giorgio Chiellini stabbed the ball over the line from close range to put the Azzurri ahead at the Stade de France in Paris, before Graziano Pelle netted a stoppage-time volley to seal victory.
"We prepared for this game in the tiniest details throughout the week and the coach gave us the right indications to beat what I think is one of the best teams in the world," Giaccherini told Sky Sport Italia.
"We legitimised the victory with many chances that we wasted, so it should have been more than 2-0."
But tactics were only half the battle for Italy, as Giaccherini revealed he provided vocal support to his international team-mates ahead of kick-off.
"Today I made the speech to the players before the game, telling them we needed heart, because tactics can only take you so far, and we had heart," Giaccherini said.
"A different player makes the pre-match speech every time, as we are a group and everyone plays their part.
"We suffered against Spain only towards the end of the second half, as we got too deep and they have exceptional players, but we had so many chances and could certainly have finished it earlier."