Alex Teixeira broke the deadlock after just three minutes in the Donbass Arena before Fernandinho doubled the lead, which proved enough to take all three points despite Oscar's late strike for the Blues.
Roberto Di Matteo's side now sit now second behind Shakhtar in Group E and Cech has called on his team-mates to start matches better.
|9/2||Oscar is 9/2 with William Hill to score anytime in a Chelsea win over Manchester United
"This had a huge impact in the game because when we had possession and lost it they had the chance to counter, to shoot, to finish. They have been doing really well and we gave them a huge lift in the third minute, then we saw them play with the confidence.
"We started slowly the same as [in the second half] against Tottenham and we got punished for that. We have to make sure we start games better than this."
The other match in the group ended in a 1-1 draw between Nordsjaelland and Juventus and Cech was glad to see the club's fate remains in their own hands with three matches remaining.
He added: "Obviously 1-1 there is a result which suits us because we dropped points here and we still play them, so we are still ahead.
"Let's forget about this one, we have a massive game at the weekend, a replay at home and hopefully it will be a different story."
Finally, the 30-year-old looked ahead to his side hosting Manchester United at the weekend, hoping that his side have learned their lesson.
"In a way what happened was a good experience for us because we have to defend better," he reflected. "We played well when we have the ball but not when we didn't have it.
"If you do this against Manchester United you are in big danger because they are the same type of team. Hopefully it was a good lesson and we learn for the weekend."