The Roma striker was included in Cesare Prandelli's preliminary squad, but was overlooked for his final 23-man party that will travel to Brazil.
Reports in the Italian media suggested Destro was asked to be on standby to cover any potential injuries, only to turn down the offer.
"Although I'm obviously disappointed, I've never refused any role in the national team," Destro said in a post on Roma's official Twitter account.
"I'll get straight down to work for a great season with my club and the national team, which remains one of my main targets."
"Prandelli had included me in the 23," Romulo was quoted as saying by Corriere della Sera.
"I told him that I was at 70 per cent, it did not seem right that a team-mate would sit out whilst being fine."
