The Brazilian midfielder scored just before halftime to give the Blues the lead, but the match ended in late disappointment, with debutant Willian also frustrated.
The loss was the club's first home defeat in a group game in a decade and saw Chelsea capitulate despite the Brazilian's opener just before halftime, and Oscar says the club's trip to Romania on Oct. 1 represents a vital opportunity to recover.
"It is bad to lose, but I think we played well," Oscar told reporters. "In the first half we were good and we started the second half very well too. Their goal destabilized the team, and then they scored another one.
"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 Willian, 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."