I am very proud to have realised my dream - Oscar
The 21-year-old scored two fine efforts in the first half to put the European Champions in control, but goals from Arturo Vidal and Fabio Quagliarella ensured the Italians left with a share of the spoils.
It was Oscar's first start for the Blues since his £25 million summer move from Internacional, and he admitted he had mixed feelings about the result.
"I am very happy with two goals on my debut but I would have been much happier if the team had won the game," he told reporters after the match.
"In Brazil, young boys dream of playing in the Champions League and I'm very proud to have realised my dream.
"I liked the reception from the fans. They're great. I hope I can keep growing and scoring goals."