A number of injures rocked the France squad heading into the finals and they were stunned as Craig Goodwin opened the scoring after nine minutes before rallying to record a 4-1 win.
Olivier Giroud scored twice to equal Thierry Henry's all-time record of 51 goals for France, while Adrien Rabiot and Mbappe were also on the scoresheet for the reigning world champions at Al Janoub Stadium.
Mbappe, who hit four goals en route to helping France to win the 2018 World Cup, was named man of the match following the victory as Deschamps hailed the Paris St Germain ace.
"Kylian of course has been one of the best players in the world for some time now and he is feeling very confident, you can see that in the way he is playing," he said.
"I knew that he was going to be ready for this World Cup, it is his competition, he knows how to make the difference.
"But he is part of a team and he has always been able to play as part of a team even though he is an individual, flair player as well. So that is great for us. I have got a lot of attackers, but Kylian is of course an outstanding one."
While Mbappe caught the eye, it was a memorable night for 36-year-old Giroud, who failed to score in all seven games en route to Les Bleus winning the final in Moscow.
Here, his two goals saw him equal Henry's record as Deschamps also reserved praise for the experienced AC Milan striker.
"I don't know if he was really thinking about the record, he tends to focus on what he does on the pitch and he has been very effective tonight," added Deschamps.
"That is great for him, he is very useful in the way he links up with all the other players in our attack and our team. Giroud did what he did best, he scores goals."
It was not all good news for France, who went into the tournament with Karim Benzema, N'Golo Kante, Presnel Kimpembe, Christopher Nkunku and Paul Pogba all missing through injury.
That list looks to have grown as Bayern Munich defender Lucas Hernandez limped off moments after Australia had broken the deadlock, Deschamps admitting he fears the issue could be "serious".
Meanwhile, Socceroos head coach Graham Arnold felt his team gave everything against a superior side.
"I think at the end of the day the quality of the French team, they are the previous world champions for a reason," he said.
"I thought that we started the game very well, physically though they are just so much bigger and faster and stronger than us today, but overall the boys did all that they could and that was all I could ask.
"That is that game gone, it is good that the other game (Tunisia v Denmark) was a draw, now it is about winning on Saturday and we have to get ready for it."