UEFA made the decision to postpone the European Championship until 2021, while all other UEFA competitions and matches for clubs and national teams have been put on hold until further notice.
Mancini said he had been talking to players as part of his preparations for Italy's scheduled March friendlies against England and Germany.
But with the coronavirus hitting Italy particularly hard, he said his focus now is on helping those in need, with the death toll in Italy passing 4,800 on Saturday.
"In the past few weeks I called some of my players, especially those who are injured and ones in doubt," Mancini told Gazzetta dello Sport. "I worked on the friendlies with England and Germany and I started setting up Euro 2020.
"I must admit that I felt disappointed when it was announced [that it was canceled].
"The film of that military convoy that took the coffins away from Bergamo was a punch in the face, the hardest and most striking image.
"No one was ready for this hell. To think that people are dying because there's a lack of beds and respirators.
"I never even thought about leaving Italy, because I feel safe here and our medics are doing heroic work. I want to feel close to those who are in difficulty.
"And I say that as a simple citizen, not as someone who has a symbolic role in Italy."
Mancini said he was heartened by the displays of solidarity among Italian citizens being widely shared on social media, where videos of communities spontaneously bursting into song from their balconies have become popular.
"I like it very much," said the former Manchester City head coach. "It's the most authentic Italy. It represents us.
"It is we who give our best in difficult circumstances, when we hug, help and put all our humanity into play.
"These people, after so much pain and fear, would have deserved the European Championship to get distracted and start again."