"We were all very shocked to see Jose go, and I felt very sad about it, both personally and professionally," said midfielder Essien in this week's Sport magazine.
"He was the manager who brought me to Chelsea and to the Premier League - he helped me a lot to develop as a player, so it has been difficult.
"But it's been a difficult few weeks for the team. We have to back our new manager, though, and go out and win games - for him, for us and for the fans."
Essien remains confident they can turn it around and mount a title challenge.
"Of course we can. We have the players and the team to do it, but we also know how hard it will be," he added.