The 4-1 defeat condemns Italy to the World Cup playoffs draw.
Azzurri captain Donnarumma said afterwards: "I'm bitter and sad, as they rightly will be. We apologise for this evening; there were so many of them and they made us feel their warmth.
"What I can say is that we need them in March and to all be together; these are too important games for us.
"Coach (Rino) Gattuso said the same thing in the locker room. We need to improve; between one half and the other, they were two different games, and we can no longer afford that."
The Manchester City keeper also stated: "It's a painful defeat, but we have to raise our heads straight away because we have two important games in March where we have a lot at stake. We need to regain confidence, start again, and I'm sure that with our coach, we'll do it brilliantly."