The current holders are in danger of getting booted out of the elite competition if they do not get a result against the Old Lady in Turin tomorrow night.
"Chelsea will arrive in a rage after failing at the weekend, but Juve is Juve and being at home always influences our rivals," the Daily Star quotes Pirlo as saying.
"We want to put the pressure on Chelsea. For this type of club, it's always a disaster to go out of the Champions League in the first phase."
The Blues sit second in Group E, level on points with leaders Shakhtar Donetsk, while Juve reside just one point below Chelsea.