The London club travel to Japan after Saturday's visit to Sunderland to play at the Club World Cup with intense pressure on interim coach Rafael Benitez to deliver.
Bringing back the trophy would help ease tension on the beleaguered Spaniard, a largely unpopular appointment among fans because of his time as manager of Liverpool.
"Not many people can say 'I won the Club World Cup' - the special competition of the Champions League winners," Cech told FIFA.com.
"We have experienced players in the team - the guys from Spain have won the World Cup, the European championship and the Champions League.
"I hope, after missing out on the Super Cup, it will be a trophy we win. With all this experience we will handle the situation."
Chelsea finally recorded a victory under Benitez at the fourth time of asking in midweek in a 6-1 rout of Nordsjaelland, although it was in vain.
After becoming the first European Champions League holders to exit at the group stage, Chelsea's 12,000-mile round trip to the Far East takes on added importance.
FIFA's seven-team competition gives Chelsea an opportunity to win some silverware, although a potential final against South American champions Corinthians stands in their way.
"Everybody was saying we are a great club, having won all the domestic trophies," added Cech. "But this is the one thing everybody kept reminding us about, not the Champions League.
"It will be a new tournament for us. We wanted to make sure that we got it one day. We will face a different style with the team from South America."
Chelsea first have to negotiate their semi-final against either Mexico's Monterrey or Asian champions Ulsan Hyundai of South Korea in Yokohama on Dec. 13.
Failure to reach the final three days later could spell disaster for Benitez and persuade owner Roman Abramovich to make another change after the sacking of Roberto Di Matteo.
Benitez has previous experience at the Club World Cup, losing out to Brazil's Sao Paulo 1-0 in the 2005 final.
Cech believes Chelsea have the character to overcome their recent troubles and become the second English club to win the title after Manchester United in 2008.
"We were almost out three times during last season's Champions League and we always came back," said the 30-year-old, pointing to their semi-final win over favourites Barcelona.
"You could see the spirit."
Chelsea's 3-2 aggregate defeat of Barcelona was achieved with a memorable 2-2 draw in the Nou Camp after being two goals down and with captain John Terry sent off after only 36 minutes.
"We showed against Barcelona the team is strong enough to cope with pressure," said Cech, who saved Arjen Robben's penalty in extra time in the final against Bayern Munich.
"We showed that in the final, we showed a great change of character in those games. A lot of people say luck involved but I don't believe in luck.
"You need to play 13 games to win the Champions League. You have to fight hard, you have to defend well, you have to be organised.
"If you are down to 10 men in Barcelona for 60 minutes then you need to really know what you're doing. We managed to do that. I don't believe that's luck." (Reporting by Alastair Himmer; Editing by Patrick Johnston)