Ancelotti was asked just as Jagielka and his teammates were warming down after victory over the Blues.
He told the London Evening Standard: "It does seem harsh. As far as quality managers go, you can't say anything against Carlo Ancelotti's ability. He is a fantastic manager.
"He chose to take a club like Chelsea and the manager doesn't normally stay for long if they don't achieve success. It is similar to Real Madrid and places like that where they have such high expectations. If you don't bring silverware home and sometimes even if you do, it's not good enough.
"It helps us that every season there isn't much speculation around the club over our manager's future."