Begovic also left Chelsea in this transfer window after being deemed surplus to requirements, but the Bosnian holds no ill-feeling towards his former club, and has backed Antonio Conte's side to show their true colours next month after a difficult pre-season.
"Chelsea would have been disappointed to lose that game [against Arsenal]. As much as people don't think the Community Shield is important, it's an important game, it's a trophy and not to win a trophy is always disappointing," Begovic told talkSPORT.
"[Antonio Conte] would not have been happy, especially immediately after the game, he would have wanted to win that game and get the season off to a really positive note. From the outside looking in, obviously I don't know, I haven't been in the camp.
"Obviously they have let a lot of players go, a lot of players have left for many different reasons, but there's still just under a month left of the transfer window. A lot of things can happen.
"I don't think you're going to see the true Chelsea until the end of August, but they can't afford a slow start. I'm sure they'll want to get off to a good start with the Champions League coming up and a Premier League title to defend too. They've got an important couple of weeks ahead."