After a 3-0 defeat to Juventus in the last round of fixtures - which saw Roberto Di Matteo replaced by Rafa Benitez - the Blues needed to win against Nordsjaelland and hope Shakhtar Donetsk beat the Italians in their final game.
And despite beating the minnows 6-1 at Stamford Bridge, the Old Lady won 1-0 in Ukraine to dump the holders out of the competition - and Cech insists the squad must take the blame rather than either manager.
"Unfortunately if you change your manager, you only change the manager, but the responsibility is on everyone," he told reporters.
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The Czech Republic keeper feels his side relinquished their trophy after slipping up at home to Juventus in a tight group, which saw them finish level with Donetsk on 10 points, but miss out due to an inferior head-to-head record.
"We had results where we didn't win and we lost away to Donetsk and to Juventus, but I think the main difference was the draw at home to Juventus where we had gone 2-0 up but we finished the game 2-2," he added.
"This is where the difference would have been. Unfortunately if you drop too many points in the group it is very difficult. We are out.
"We knew what could happen prior to the game. The damage had been done before. We did what we could. We had a good performance and goals."
Cech believes Chelsea must now focus on domestic competitions and the Europa League to salvage their season.
"We could only hope and, unfortunately, the other result did not go our way so we we are out," he coninuted. "Now we need to focus on other competitions."