Inter defender Diego Godin felt "exposed" to coronavirus until the last minute, saying Serie A tried to continue until it became "unsustainable".
Serie A was suspended on March 9 due to the coronavirus pandemic, which has hit Italy hard.
A day earlier, Inter suffered a 2-0 loss to Juventus and on March 12, defender Daniele Rugani tested positive for Covid-19.
Godin said there was a push for football to continue until the situation was no longer under control.
"We were exposed until the last moment. They kept pulling the rope to see if you could continue playing, until the situation was unsustainable," Godin told ESPN.
"The health system collapsed, there are no intensive care beds to attend so many critically ill people and people who may have another illness, they cannot attend to them, so many professional doctors."
Godin added: "We continued playing for several weeks, we continued training, playing behind closed doors, until the positive of a Juventus player was detected and we and the Juventus players were quarantined.
"There the championship was stopped. Surely in that match there were other players who would already be infected, so they directly quarantined all of us."
Italy has recorded more than 92,400 cases of coronavirus, reporting 10,023 deaths.
While Serie A was slow to stop games being played completely, early signs suggest they won't be rushing any potential return, with May 3 even believed to be too soon by some.
"The forecasts that made us think we could resume sports competitions in late April or May, have been too optimistic given the evolution of the health emergency," Italy's minister for sport Vincenzo Spadafora told Rai 3's Chi l'ha visto.
"I can say for certain that, if the resumption of sporting events will exist, it will certainly start again behind closed doors.
"It's not possible to think otherwise, but I also have some doubts with respect to the date of May 3. Unfortunately, this medical emergency is constantly related to its evolution. We have to adapt our decisions very often to the epidemic.
"The final choice will be down to the FIGC, but it's unlikely that it will be able to resume in the beginning of May.
"The federation might decide to postpone the games until the late summer, I have read suggestions about July and August, but the situation is complicated.
"After all, the rest of the footballing world has given us some more time to understand the emergency and now I imagine it will move forward with the necessary caution."