The Stamford Bridge side are seven points adrift of league leaders Manchester United and defeat at home to the Wanderers on Wednesday would see Ancelotti's men drop to sixth in the Premier League.
Chelsea will be without Alex, Yuri Zhirkov and Yossi Benayoun for the game against Bolton, while former Wanderers striker Nicolas Anelka could be forced to miss the visit of his former employers with a knee injury.
However, Cech believes the Italian coach can turn the club's fortunes around and reignite their title push.
"He's got lots of experience," said Cech on Ancelotti. "There was a lot of pressure when he was manager of AC Milan.
"Last season there was a period where there was a lot of pressure here and yet we turned things round and won the double. We will try to do the same thing."