The Blues lost 4-1 on penalties at Wembley Stadium, the Italian succumbing once again to the Gunners in the English national stadium after losing the FA Cup final in May.
"For sure, there is disappointment to finish for the second time with 10 men against Arsenal," Conte told Sky Sports News. "Before the FA Cup, and now the Community Shield.
"I did not see the images [for the Pedro red card] and I did not see the yellow card for Willian. A lot of people told me the penalty was clear, so for sure there is a bit of frustration. We have to respect the refereeing decision but sometimes this decision makes you a bit angry.
"[Madley] tried to explain to me about his decision but there was no time because I also wanted to ask him why there wasn't a penalty and the yellow card for Willian. But then we would have spoken until 9 o'clock."
Chelsea have lost their last four Community Shield matches, last winning the trophy on penalties in 2009.