Newcastle's Sandro Tonali was the only Italian player to score from the spot as Bosnia and Herzegovina found the net with all four of their penalties in a Tuesday to forget for Italy.
The Italians failed to reach Russia 2018 and Qatar 2022 and are the first former winners to miss out on three consecutive World Cups.
It was an emotional night for the side who were toothless through the game before collapsing in the penalty shoot out.
Donnarumma, who failed to save any of the penalties he faced, has now sent a message to fans who will be distraught after such a result.
“Last night, after the match, I cried,” wrote the Manchester City star.
“I cried with disappointment at not being able to take Italy to where it deserves to be. I cried because of the immense sadness I’m feeling together with the entire Azzurri squad of which I am proud to be captain, and which, I know, at this moment, you too are feeling, supporters of our national team.
“Now words don’t mean much, it’s true. But there’s one thing I feel strongly inside and want to share with you. After such a great disappointment, we must find the courage to turn the page once again. And to do that, we need a lot of strength, passion and belief. Always believing. That’s the engine that drives us forward because life knows how to reward those who give everything, holding nothing back.
“And this is where we must start again. Together. Once more. To bring Italy back to where it deserves to be.”
The Manchester City stopper will only be 31 by the time 2030 rolls around and he may get his chance at the next World Cup if Italy can step up and deliver for their nation.