The west London side led 3-0 with 50 minutes gone before two Wayne Rooney penalties and a dramatic equaliser from Javier Hernandez saw the game finish 3-3.
Cech told Chelsea's official website: "I felt sorry we didn't get the job done.
"If you are 3-0 up you should be able to win.
"But it was showed once again that you can't take anything for granted in football. Everything can change within a short spell of time."
Andre Villas-Boas criticised referee Howard Webb for awarding United's second penalty after an incident between Branislav Ivanovic and Danny Welbeck, but Cech refused to give his thoughts on the decision.
"I won't comment on it," he said.
"We are not allowed to make comments on referees, so whether the penalty should or, should not have been given, is on others' opinion.
"I have my view but don't want to judge the referee."
The draw left Chelsea sitting 14 points behind league leaders Manchester City, while second-placed United are now just two points behind Roberto Mancini's men.