From the resulting free kick, debutant Sead Kolasinac headed the Gunners level to take the match to penalties after 90 minutes.
The shootout - the first in English football to follow the ABBA format - saw Chelsea miss back-to-back penalties to allow Olivier Giroud to win the match from the spot.
Conte told BBC Sport after Sunday's game: "I didn't see the situation [with the sending-off].
"For me for this reason it is very difficult for me to say something about this decision. This is the second game, after the FA Cup, that we finish with 10 men.
"We are working, we are trying to do our best. We had a tough pre-season, between the six days until we start the league it is important to be focused on the next game."
Chelsea have lost their last four Community Shield matches, last winning the trophy on penalties in 2009.