The Brazilian was disappointed with the result but was happy to get his debut out of the way.
Speaking to 'Globe Esporte', Willian said: "It's good to make your debut but it would be even better if it was a winning one.
"Now we have to raise our heads and try to win the next game. I know that I have to try and get better.
"I can't stop, I always have to try and keep a good pace and that's what I'll do."
Despite the result, Willian insists he will continue to try and impress manager Jose Mourinho.
Willian added: "I have to show every game, every training session, and then Mourinho will be able to believe in me."