Chelsea thrashed FC Nordsjaelland 6-1 to grab a first win of Rafael Benitez's reign, but it was not enough as Juve claimed a 1-0 win at Shakhtar Donetsk.
"We knew that it could happen," Cech told Sky Sports 2. "We knew that if Donetsk didn't win then we would be out. Unfortunately that is the reality.
"We did what we could. We had a good performance and scored six goals."
Chelsea's fate had rested in the hands of Shakhtar after a stuttering campaign that saw the Blues lose at Juventus as well in Ukraine.
Cech, however, believes the opening day 2-2 home draw with the Italian champions was the most damaging result, when his side squandered a 2-0 lead.
"You have results where we lost away to Donetsk and Juventus but I think the main difference was the draw against Juve at home," said Cech, who saved a penalty when the game was still goalless.
"We were 2-0 up and then ended 2-2. If you drop too many points in the group then you can't go through."
Cahill echoed the thoughts of his goalkeeper, adding: "The two results against Juve were damaging for us.
"I've just said that with 10 points sometimes you through but that was not to be in our group. We had to do more than that."