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The Blues could only draw with Atletico Madrid in their final match on Tuesday, meaning they qualify in second place behind Roma.
The Brazilian winger missed a glorious chance to earn all three points and while he was disappointed with the result, he insists Chelsea’s focus is now making up ground on runaway Premier League leaders Manchester City.
"No, we are not happy," he said.
"We wanted to finish first. We tried to create some chances in the second half.
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“We have to play against the big teams if we want to be the champions.”
Chelsea star Willian
"We have this really good team, a strong team. Our desire was to finish first.
"We are now second, it's OK, so let's think about the Premier League and the Cups."
Chelsea will be in pot 2 for Monday’s draw and as they cannot be drawn against another English team or Group C colleagues Roma, they face the prospect of a knockout tie against Barcelona, PSG or Besiktas.
All three teams would represent a tricky route to the last eight but Willian is adamant that there’s nobody in the competition that his side fear playing.
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He added: “We are Chelsea, we are a big team like them.
"We don't have a choice. We have to play against the big teams if we want to be the champions."
Antonio Conte’s men are currently third in the Premier League and return to domestic action on Saturday as they travel to fierce rivals West Ham (12.30pm).