The 29-year-old goalkeeper was powerless to prevent the Blues conceding with less than five minutes on the clock, as Steven Pienaar - making his second home debut for the Toffees since returning to the club on loan from Tottenham in January - fired David Moyes' side into an early lead.
Andre Villas-Boas's side enjoyed large portions of possession, but could not make their dominance count, and when Denis Stacqualursi doubled the home side's advantage in the second period, Chelsea were dead and buried.
"When you lose a game 2-0 and you are Chelsea Football Club playing for the Champions League and with big expectations, losing is not good enough and the performance was not good enough, that's why we lost," Cech told the club's official website.
"We took so many passes side to side and we never really opened them up. In the second half we tried to play more direct but they were fighting well and kept organised, and 1-0 up so early became so much more difficult to break."
The defeat - Chelsea's first of 2012 - leaves the club now languishing in fifth place in the Premier League table, behind Arsenal on goal difference in the race for that all-important final Champions League spot.
Their current form leaves a lot to be desired, and without a single win in the past month, the most alarming thing will be the Blues' lack of cutting edge in the final third on Saturday, leaving little to inspire the club's increasingly blunt attack.