The Blues goalkeeper also challenged his team-mates to help the eighth manager he has worked under win over the fans after abuse was directed at Rafael Benitez in the Spaniard's first game in charge at the weekend.
The ruthless axing of Roberto Di Matteo may have come as a shock for some of their younger team-mates, who were given only three days to get used to a new boss before Sunday's Barclays Premier League clash against Manchester City.
Asked if it was difficult getting used to new man in charge, Cech said: "You adapt or you're out. It's as simple as that.
"You're here to play, you're here to do what the club and manager wants you to do. If you don't like it, you can leave.
"I want to play so I do everything I can straight away so that the manager has no option but to put me in goal.
"It's the way it works for everybody because, if you stay sad and don't do the right things, you can end up on the bench.
"As a player, you need to do the right thing all the time."
All of Abramovich's managerial changes have been controversial, but the latest was in a whole different league.
Sacking the man who ended Chelsea's wait for a Champions League title was bad enough for many supporters.
But replacing someone who was an icon as a player and coach with a hate figures in the club's modern history was beyond the pale.
Cech added: "It is up to us to have a good run of results for fans to change their minds.
"The manager surely deserves to have a chance and it's up to us to make things happen."