Last season's champions thrashed Nordsjaelland 6-1 on Wednesday night but it was not enough to see them through to the last 16 after previous poor results in Group E.
Rafael Benitez's men now drop into the Europa League knockout rounds and Cech says they will not be taking the competition lightly.
"It is still a European competition where you have a chance to win a trophy," the Czech keeper told his official website.
"In nine years I have spent here we have never played in it, so why not to try to win it? To have the Europa League trophy also counts."
Cech says it was a "huge disappointment" for Chelsea to crash out of the Champions League but admits their group campaign was lost before Wednesday's game.
He added: "If we had reached the last 16 or quarter-finals of the Champions League and had been knocked out then, the disappointment would have been the same as the quarter-finals are no success for a club like Chelsea.
"Naturally, we all feel very sorry now but we know that we had lost it earlier, not in the final match. There it was difficult to chase it.
"It is a huge disappointment that we won't have a chance to defend the trophy. But there's nothing we can do now, that's football."
Wednesday's win ended a run of six games without a win in all competitions and Cech hopes the success will hand Chelsea a psychological boost.
"Finally we played a good game," he said.
"We put pressure on the ball, we forced the opposing players to make mistakes, we converted our opportunities. We scored a lot of goals.
"But we need to confirm this right against Sunderland and then in Japan at the (FIFA Club) World Cup.
"I believe this win will help us psychologically."