Gasperini said he was ill as Atalanta beat Valencia 4-3 behind closed doors at the Mestalla in the Champions League on March 10, when the Serie A side reached the quarter-finals with an 8-4 aggregate victory.
The 62-year-old said he feared for his life as he struggled with COVID-19, which has killed more than 371,000 people worldwide.
"I was scared. The day before the game I was sick, the afternoon of the game worse. The two nights after I slept little," Gasperini told La Gazzetta dello Sport.
"I didn't have a fever, but I felt shattered. Every two minutes an ambulance passed. It seemed to be like a war.
"At night I thought, 'If I go in there, what happens to me? I can't go now, I have so many things to do.' I said it to lighten the mood, but I really thought so."
Gasperini said he also lost his sense of taste, a common symptom of coronavirus.
The former Inter boss said a recent test showed he had coronavirus antibodies, confirmation he battled the illness earlier this year.
"Ten days ago serological tests confirmed that I had COVID-19," Gasperini said.
"I have the antibodies. It doesn't mean that they are now immune."
Serie A is due to resume on June 20, with Gasperini's Atalanta sitting fourth in the table.