The Italian Football Federation (FIGC) confirmed on Saturday that Conte had been the target of online abuse after Claudio Marchisio was hurt during a training session.
Juventus club patron John Elkann suggested Conte's intense training methods were to blame for the injury to Marchisio, who was initially suspected to have ruptured knee ligaments only for his club to subsequently confirm otherwise.
Italy went on to draw 2-2 with Bulgaria later on Saturday, Brazil-born forward Eder marking his controversial maiden international call-up with a late equaliser in Sofia.
Addressing the criticism he has received, Conte said: "These things I won't forget because they hurt me. Having said that I only ask to do what I have always done.
"I always worked hard in my life, sometimes delivering good results, sometimes less, but I always worked hard.
"So the only thing I'm asking is to let me be free to work with this team. I think that I was called to manage Italy to work, so I would like to be able to work in peace and then be judged for my results.
"In these days I heard some underhand statements and those I can't forget, even because I have a memory like an elephant.
"Now we will focus on Tuesday's game against England. It is a prestigious friendly in which I want to test some of the new players who have joined the national team for the first time.
"So it will be an important international test to verify if the players I called up deserve to stay in the national team."
Conte has added Davide Santon and Ignazio Abate to his ranks, while England boss Roy Hodgson will be forced to call upon some of his fringe players.
Hodgson's men eased to a 4-0 victory over Lithuania in their latest Euro 2016 qualifier on Friday, making it five wins out of five in Group E.
However, Danny Welbeck, James Milner (both knee) and Raheem Sterling (toe) have since pulled out of England's squad, and Ryan Bertrand has been included to cover for left-back Leighton Baines, who has returned to Everton as previously planned.
"We've got a tougher test ahead of us against Italy and we will be playing that game with players we wouldn't normally rely upon," Hodgson told FA TV.
"Italy and Ireland [who England face in June] will be to some extent experimental and a chance [for players] to break in to what we think is our best XI."
