Ventura replaced Antonio Conte last month and pledged to carry on the good work of the current Chelsea manager following the Azzurri's impressive march to the quarter-finals of Euro 2016.
But goals from Manchester United striker Anthony Martial, his first for his country, and Arsenal's Olivier Giroud either side of Graziano Pelle's 21st minute strike gave France a 2-1 half-time lead.
After Donnarumma replaced Juventus legend Gianluigi Buffon for the second period, the 17-year-old made one impressive stop before making his first major error for the national side.
Barely 10 minutes before the final whistle, Donnarumma came off his line at his near post to anticipate a Layvin Kurzawa drive across the Italian goalmouth, only for the Paris Saint-Germain left-back's strike to spin into the far corner of the net for his first international goal.
Ventura admitted he was "fairly satisfied" with his side's performancegiven he had spent "only three days working with the squad".
He also gave Donnarumma a gentle hint that he could be well on the way to replacing Buffon in the near future.
"He's a player with huge potential. I wasn't going to bring him with us just to sit on the bench," said the 68-year-old coach.
"He's young, but full of talent and it's only right he gets to experience the Italy dressing room."
'Can do better'
It was France's first outing since Les Bleus lost the Euro 2016 final on home soil to Portugal.
And coach Didier Deschamps said: "I'm happy, we can always do better but it's not too bad when you put three (goals) past an Italy side that gives little away."
Italy, ousted at the quarter-final stage of Euro 2016, begin their 2018 World Cup qualifying campaign on Monday away to Israel in Haifa.
They looked comfortable in the early stages but a defensive mix-up between Juventus pair Andrea Barzagli and Giorgio Chiellini allowed Martial to pounce on the gift and beat Buffon one-on-one.
Yet Italy hit back almost immediately, Inter Milan striker Eder flying past N'Golo Kante down the right to deliver for Pelle to spin around Raphael Varane and beat rooted keeper Steve Mandanda on 21 minutes.
The goal, Pelle's fourth in his last seven Azzurri appearances, must have calmed his fears that a recent move to the Chinese Super League would harm his Italy chances.
But France were soon back in front, Chiellini losing sight of Giroud on a corner for the Gunners marksman to beat Buffon with a well-taken volley.
Donnarumma became the youngest ever goalkeeper for Italy and the youngest Azzurri player since 1911 when he replaced Buffon at half-time, and didn't have to wait long to be called into action.
Donnarumma was quickly down to smother a Dimitri Payet effort that bounced in front of him.
Ventura then introduced Marco Verratti, the PSG midfield star making his first Azzurri appearance since qualifying for Euro 2016, which he missed through injury.
But his arrival failed to produce the desired effect as Pelle nodded Antonio Candreva's cross over the bar.
Ventura further underlined his aim to inject fresh life into the Azzurri by replacing Eder with Torino striker Andrea Belotti for the final quarter hour.
But after Belotti failed to capitalise on Alessandro Florenzi's volleyed cross, France added a third.
Manchester United midfielder Paul Pogba threaded a great ball through for Kurzawa, who beat the keeper with a curling shot after the teenager came too far off his line.