Milan threw away the lead to lose 2-1 to Torino on Thursday night.
“It's a defeat that burns. It's a dark day and I struggled to sleep last night," Donnarumma told Sky Sport Italia.
“Yesterday I saw the team give everything, I'm sorry for everyone, the fans included. We have to follow the Coach because we're working well and we have great ideas on how to play. We must follow him.
“Giampaolo's a great Coach. I'm sorry because yesterday we had a great game and we didn't deserve to lose.
“We're all with him. It's normal to struggle a bit at the start with new ideas and new players, but we should continue to follow him. We're all with him.
“After the first goal, we fell apart. We need to improve on this. If we'd remained compact, we would've been able to take the win home."