Benitez admitted on Sunday 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."
"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."