"Emergency is not involved in this episode. We have 1,000 workers [in Afghanistan] and I would like to know who is responsible for this plot," Garatti said after his release.
"It is possible the weapons could get in the hospital without our knowledge, we are not there 24 hours."
The arrest of the aid workers had caused a public outcry in Italy.
Silvio Berlusconi, the Italian prime minister, sent a letter to Hamid Karzai, the Afghan president, and dispatched a special envoy to seek the men's release.
On Saturday, thousands took to the streets in central Rome to demand that charges against the doctors were dropped.
"They are really relieved. They were treated in a good way but they were not able to contact their families or colleagues to tell them how they were doing"
director of Emergency
Cecelia Strada, the director of Emergency, told Al Jazeera the men were "very, very happy."
"They are really relieved. They were treated in a good way but they were not able to contact their families or colleagues to tell them how they were doing," she said.
The release was welcomed by Franco Frattini, the Italian foreign minister.
"We have obtained what was our main aim, that is the release of our three compatriots, without putting into question our solidarity with Afghan institutions or with the international coalition," he said in a statement.
"This is the result of intense diplomatic activity conducted in a professional manner and with discretion."
Speaking from the Afghan capital, Al Jazeera's James Bays said that pressure from Italian authorities appeared to influenced the decision to free the men.
"Things seemed to have moved very fast in the last few days," he said.
"President Karzai has had a letter from the Italian Prime Minster, he has had a visit from the Italian special envoy. Public pressure in Italy seems to have had an effect."
All but one of the men's six Afghan colleagues who were arrested in the incident had also been released on Sunday, Afghan officials said.