Italy, playing their first game under new coach Giampiero Ventura, were trailing 2-1 at Bari's Stadio San Nicola when Donnarumma entered the fray but he had little to do until he smothered the ball at Andre-Pierre Gignac's feet.
However he was beaten inside his near post by Lavyin Kurzawa's shot for France's third goal in the 81st minute, although shortly afterwards he did well to stop a Paul Pogba free kick which found a hole in the Italy wall.
"Buffon told me to stay calm, do what I know and to have fun," Donnarumma told RAI television. "I can't describe it. I want to thank the coach for this opportunity and my debut. I am quite emotional about it.”
Ventura, who had only three days to work with his squad, made few tactical changes to the team he inherited from Antonio Conte which reached the Euro 2016 quarter-finals, beating reigning champions Spain on the way.
Anthony Martial had put Euro 2016 runners-up France ahead after poor defending by Italy, Graziano Pelle levelled with a shot on the turn but Olivier Giroud put the visitors back in front after more unusually slack defensive work by the hosts.
It was the first international to feature a so-called video assistant referee (VAR) to help the officials on the pitch.
FIFA said it was an "offline" test in which the VAR was able to communicate with match referee Bjorn Kuipers but the game would not be stopped to check replays.
"FIFA is expecting this first test to provide conclusions and directions for future VAR training sessions with elite referees," soccer's world governing body said in a statement.
(Writing by Brian Homewood; Editing by Ken Ferris)
