League One Bradford City produced one of the biggest shocks in the FA Cup history by battling from 2-0 down to win 4-2 at Stamford Bridge on Saturday and reach the fifth round, a result that left Mourinho "ashamed" and "embarrassed".
But Cech insists that Mourinho's men cannot afford to dwell on the setback as Liverpool prepare to make the trip to London in midweek for the second leg of a League Cup semi-final tie that hangs in the balance at 1-1.
"We need to take it on the chin and pick ourselves up," the Czech Republic goalkeeper goalkeeper told the club's official website.
"It's up to us. We have put ourselves in this position and we only have ourselves to blame for what happened.
"We play at home on Tuesday and we would like to use that as an advantage. We need to clean the mess up."
Like Mourinho, Cech was magnanimous in the defeat at the hands of Bradford, who reached the 2013 League Cup final with wins over the likes of Arsenal and Aston Villa.
He added: "It's one of the biggest ever surprises in the FA Cup.
"Obviously we are not proud of the result but I wouldn't want to take anything away from the Bradford team because they came here, they fought hard for their luck, they got chances and they scored four goals. Credit to them.
"I've been here for more than 10 years and every year you can see these kinds of results in the FA Cup. That’s why I have always said it's special. This can always happen and unfortunately for the first time I was on the wrong side of that. That's the way it goes."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.