The former Chelsea boss took over at the San Siro on Thursday after Gian Piero Gasperini was fired only three games into the new Serie A season.
"It was good to start off on the right foot," said Ranieri. "These guys needed to find a way to win and gain some self-confidence."
Goalscorer Diego Milito was keen to praise Ranieri's instant impact, but the Argentine also suggested that former boss Gasperini had been unfortunate with his dismissal.
"Let's hope this marks a turnaround," he said. "Ranieri's arrival has given us a lot of enthusiasm, mostly at the psychological level. But I want to share these three points with Gasperini, too. They're also his, because he did a great job but unfortunately we weren't able to transmit that to the pitch."
Inter's next match is a Champions League group fixture against CSKA Moscow.