The Blues goalkeeper also challenged his team-mates to help the eighth manager he has worked under win over the fans following the savage abuse directed at Rafael Benitez in the Spaniard's first game in charge.
But 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 the top-of-the-table Premier League clash against Manchester City.
Asked if it was difficult getting used to new managers, 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'm here to play, 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.
"That's the way I work and is 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 and you're not playing and it will be even more disappointing.
"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 agonising wait for Champions League, Di Matteo, was bad enough for many fans.
But replacing someone who was an icon as a player and manager with one of the most disliked figures in the club's modern history was beyond the pale.
The jeers of disapproval at the mention of Benitez's name on Sunday were almost deafening, while the chants and placards left no doubt about how unwelcome the former Liverpool boss was at his new club.
The 52-year-old will run the gauntlet again in tomorrow night's derby with Fulham, with the leaders of supporters' groups indicating that they would show no mercy to him.
Benitez knows that only wins would silence the boo boys, and Cech insisted it was the responsibility of Chelsea's players to produce them.
"It is up to us to have a good run of results for them to change their minds," he said.
"The manager surely deserves to have a chance and it's up to us to make things happen and make the fans happy."
Sunday's draw with Manchester City left Chelsea five points behind leaders Manchester United with a third of the season gone, and a run of victories after just two in nine games would do more than get supporters onside.
"This is the ideal situation and scenario," Cech said.
"When you have a change of manager, you need that impulse from everybody to get out of the situation we're not comfortable in.
"The ideal scenario is to get a run of results and then, suddenly, the season will look different."
With no let-up to a punishing calendar of fixtures, Chelsea could quite easily find themselves cut further and further adrift.
Cech added: "We know we now have two derbies which are very difficult games.
"Before we take off for Japan, we need to get as many points to be in a good position because, obviously, we will be away, there will be a difference between games played, and the table will look different.
"The calendar will be really stretched and heavy for us, with a lot of games, so we need to be in the best position possible when we come back from Japan."
Chelsea enjoyed a fitness boost when Gary Cahill returned to training after illness prevented him starting at the weekend.
However, Daniel Sturridge is unlikely to be fit for the Fulham game.