Nevertheless, their visit was "a bit like giving them a window onto a wider stage of Christian life," Santobonio said.
Other children had arrived in the early morning from an impoverished town near Naples to deliver a letter to Francis, said Andrea Lacomini from UNICEF, which organised the excursion.
"He loves children, he is the pope of the children, so we are waiting for him. We're sure he will get better," Lacomini told AFP.
"We need an important leader like him, because at this time there aren't many heroes in the world," he added.
"He's the only one who talks about peace."
Despite failing to appear at the window, Francis addressed his youngest well-wishers in his message.
"I know that many children are praying for me; some of them came here today to 'Gemelli' as a sign of closeness," Francis wrote.