The champions went out of the competition just 200 days after they won it in Munich under former manager Roberto Di Matteo.
Di Matteo was sacked last month, and replaced with former Liverpool boss Rafael Benitez in a deeply unpopular move for the club faithful, but Cech said the players were ultimately responsible for their poor performances.
"Unfortunately if you change your manager, you only change the manager. But the responsibility is on everyone," he said after a 6-1 defeat of Danish side Nordsjaelland at Stamford Bridge was not enough to see Chelsea through after Juventus beat Shakhtar Donetsk 1-0.
"We are all in the same boat, the manager and the players. The responsibility is the same for everyone. You are a team," added Cech, the stand-in captain in the absence of injured duo John Terry and Frank Lampard.
The goalkeeper was echoing the view of Terry, who had written in the match programme that it was time for the players to stand up and be counted.
"Let's not beat around the bush. No wins in six games is simply not good enough and since I have been here I have not experienced a run like this," he declared. "We as players have to stand up and take responsibility - stand up and stay together."
Chelsea finished third in Group E and qualified for the Europa League after ending level on points with second placed Shakhtar, who beat them in Ukraine and went through on their head-to-head record.
The continent's second string club competition could prove a distraction to the club's Premier League ambitions, with champions Manchester City now out of Europe altogether, but Benitez said it would not be dismissed.
"The Europa League is not important if you don't win it but if you are in the semi-final or final, everyone wants to win it," said the Spaniard.
"It's an important competition at that stage. So, if we get there, we'll do our best to win it."
