Les Bleus benefited from the competition's first use of VAR technology when they were awarded a debatable second-half penalty, which was converted by Antoine Griezmann.
Although Australia captain Mile Jedinak levelled from the spot four minutes later following a Samuel Umtiti handball, goal-line technology was used when Paul Pogba's deflected shot crept over the line in the 81st minute.
"It was not easy, but winning the first match is very important," Deschamps told L'Equipe. "It was complicated today with a team who gave us a hard time. It's hard to explain everything. We missed a change of pace, a little juice.
"At the end of the match, we had a few more opportunities. It's hard for everyone, apart from the first match of the Russians against Saudi Arabia. We did the job. But we can do better, do a lot better."
France return to action on Thursday night against Peru.