The 25-year-old moved to Stamford Bridge from Russian side Anzhi Makhachkala on a five-year deal during the summer transfer window and is starting to make his mark in Jose Mourinho's side.
Willian played the full 90 minutes of Chelsea's 2-0 victory over Arsenal in the fourth round of the Capital One Cup and admits he was delighted to be a part of the team's progress.
Cesar Azpilicueta and Juan Mata struck in each half as the Blues reached the last eight but Willian believes the win was all the more valuable considering Arsenal's prolific start to the season.
"Playing a derby as important as that one was a different feeling," he told French football site Lancenet.
"I am very happy to have achieved that beautiful win and to have advanced to the next round.
"Arsenal's team have a lot of quality, which is why they top the league, beating them at this moment makes our victory even more commendable."
Late summer-signing Willian has made three appearances in the Premier League to date, scoring on debut against Norwich, and hopes to stake a claim for a permanent starting position.
"I am happy with myself, as I think I am improving every match," he added. "I ran a lot, I managed to create some good plays and help the team.
"I'm feeling physically better and slowly becoming more confident.
"I am sure I'll grow even more, improve with every game. What is important is that I am happy and that I am earning my place."
Willian could feature on Saturday as Chelsea travel north to face Newcastle at St James' Park in the Premier League's lunch-time kick-off.