But the Brazilian has improved greatly since then, with his most impressive performances coming in the wins over Liverpool and Southampton, where he came off the bench to help the Blues to a 3-0 win.
When asked whether it was likely that Willian would improve, Chelsea goalkeeper Cech said: "Yes. You always give players a few months to settle because the Premier League is different to anywhere else.
"Questions were raised because he came from Anzhi Makhachkala where he was unlucky with injuries and he didn't play much.
"But from day one he has worked really hard. He was waiting for his chance and since the first start you can see he is taking his opportunity.
"He has been absolutely brilliant. He keeps working for the team, making the difference, scoring goals, defending. I thought I'd never see anyone running more than Ramires, but he's really there.
"It's fantastic to see he's enjoying his football, enjoying his life in the club. This is important.
"It's very pleasing to see his progress."
Mata made his displeasure clear on New Year's Day when he was substituted in the 53rd minute of the 3- 0 victory at St Mary's Stadium.
The Spaniard did not shake Jose Mourinho's hand and he flung his arms in the air from the bench in the direction of the pitch, where the Chelsea manager was standing.
Press Association Sport understands that on Thursday, Mata's agent called Chelsea in an attempt to get the club to clarify the reporting of Mourinho's post-match comments regarding the player.
"I want to keep him. I don't want him to go. That is my opinion, my wish, but my door is open," the Chelsea manager said.
Some had interpreted that as a sign that Mourinho was willing to sell the player.
Another player who is struggling to get into the team because of the form of Willian, Oscar and Eden Hazard is former Genk player Kevin De Bruyne.
The Belgian wants to leave Chelsea after making just two Barclays Premier League starts in two years, but it is understood that Mourinho is unwilling to sell the player despite interest from Wolfsburg, Atletico Madrid and Juventus.
De Bruyne is likely to get a run-out on Sunday when Chelsea take on Derby in the third round of the FA Cup.
The Blues will be without injured duo Frank Lampard and Branislav Ivanovic, who are out until the last week of January.