The Brazilian midfielder scored just before half-time to give the Blues the lead but the match ended in late disappointment, with debutant Willian also frustrated
Wednesday's loss was the club's first home defeat in a group game in a decade and saw them capitulate despite the Brazilian's opener just before half-time.
Now their trip to Romania on October 1 represents a vital opportunity to recover, says Oscar.
|14/1||Chelsea are 14/1 with William Hill to win the Champions League
"Now we have to recover in the next round, we have to win."
The defeat to Basel also saw new signing Willian make his debut but Oscar's countryman was disappointed to see it end as it did.
"It's good to debut [but] it would be even better if it was winning," said the attacker, who was replaced by Juan Mata after 67 minutes while the Blues were in the lead. "Now we have to raise our heads and try to win [the next game].
"Debuts always have a bit of anxiety but I think I could show some of my football.
"I know that I have to try get better every day. I can't stop, I always have to try and keep a good pace and that's what I'll do. I have to show every game, every training session, and then [Mourinho] will be able to believe in me."