The Blues completed the league and cup double after beating Portsmouth, who were relegated from the Premier League, 1-0 at Wembley.
A goal from Ivorian marksman Didier Drogba handed them their second consecutive FA Cup title but they could have struggled had Portsmouth's Kevin-Prince Boateng converted a penalty three minutes earlier.
The Ghanaian midfielder stepped up but saw his effort saved by Cech.
"That was the key moment because if Portsmouth went 1-0 up it would have been more difficult for us," Ancelotti said.
"But Cech saved the penalty and we scored with Drogba, which made it easier."
The Italian coach was over the moon after guiding Chelsea to the double in his first season at Stamford Bridge.
'This is a fantastic victory for me, I am very happy in my first time here in England," he added.
"I am lucky I had a very good career with fantastic clubs and this year I was happy to work in a fantastic club with a fantastic atmosphere."