The 21-year-old Brazil international struck two goals against the Serie A holders, but believes that a victory would have made the performance even better
Having moved to Stamford Bridge in the summer from Brazilian club Internacional for a fee in the region of €31 million (£25m), the youngster has so far been used sparingly by boss Roberto Di Matteo as he looks to slowly integrate him into the side.
However, against Juventus, it was Oscar who managed to grab both goals as the Blues were held at home by Serie A reigning champions Juventus yet the 21-year-old was more than happy with his display.
"I am very happy with two goals on my debut but I would have been much happier if the team had won the game," Oscar told reporters.
"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."
After his performance, he also came in for some praise from his new team-mates and centre-back David Luiz believes that there is more from Oscar to come now that he starting to adjust.
"I think he has a great future. Not only with Chelsea but with the national team, too. So tonight he showed who is Oscar," he said.
"I know how hard it is when you don't speak the language, to go out to a restaurant or something and you don't know what to do if you're waiting for food or something.
"But now I'm trying to help Oscar and he can help Chelsea, too."
Goalkeeper Petr Cech also felt that the midfielder played well in what was a sizeable test against a side unbeaten in Italy for over a year, arguing that he looks as if he is more than capable of justifying his huge price-tag.
"He's a very talented guy and it's great for him to score two goals because, for his age, he cost a lot of money," he added.
"So there is a lot of pressure on him, and it's great for people to see how good he can be for this football club and today I was very pleased that he got his goals and he played very good football.
"He played nice, simple football. He's always in the movement, always available and really efficient."