The 17-year-old replaced World Cup winner Gianluigi Buffon in Thursday's 3-1 defeat by France in Bari.
AC Milan star Donnarumma was born 484 days after Buffon, 38, made his international debut on 29 October 1997.
"He's a player with huge potential," said new Italy coach Giampiero Ventura. "I wasn't going to bring him with us just to sit on the bench."
Donnarumma replaced Juventus legend Buffon at half-time, with Italy already 2-1 down at the Stadio San Nicola.
"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."
The 6ft 5in Donnarumma made one impressive stop before France added a third in the 81st minute.
He came off his line at his near post to anticipate a Layvin Kurzawa drive across the Italian goalmouth, only for the Paris St-Germain left-back's strike to spin into the far corner of the net.
France's first two goals came from Anthony Martial and Olivier Giroud, with Graziano Pelle netting for Italy in between.
Buffon has tipped Donnarumma to succeed him as Italy's first-choice keeper.
Italy's most-capped player, Buffon has made 162 appearances for the Azzurri over 19 years and helped them win the World Cup in 2006.
Teenager Gianluigi Donnarumma said he was "quite emotional" after becoming Italy's youngest-ever goalkeeper.