Last season's Champions League winners must overcome a deficit to reach the Europa League quarter-finals after falling to a 1-0 loss in Romania last night after Ryan Bertrand conceded a penalty, scored by Raul Rusescu.
The Blues have no time to wallow in self-pity, though, following the poor performance as their FA Cup defence continues at Old Trafford in their second game in four days.
"It's the best way to forget about this defeat," Cech told Chelsea TV.
"The games are coming thick and fast. We won't have much time to prepare, but we'll get a little bit of rest and hopefully we'll have a good performance on Sunday.
"They are the favourites for the game, but it's the FA Cup and in the FA Cup not every time do the favourites win.
"We're still the holders, so we'll try to keep our trophy as long as we can."
United, the runaway Barclays Premier League leaders and 19 points clear of fourth-placed Chelsea, last won the FA Cup in 2004.
Since 2007 the Blues have dominated the competition, with four wins in six years.
Following the highs of Wembley and Munich last May, Chelsea are enduring a torrid 2012/13 season and became the first holders to exit the group stage of the Champions League last November.
The FA Cup has not been plain sailing, either.
The Blues needed a replay to defeat npower League One Brentford, then claimed a 2-0 win at Middlesbrough in a fifth-round tie overshadowed by comments made by interim manager Rafael Benitez.
The Spaniard hit back at his continual barracking by the club's supporters, told them to use their energies to support the team as he is to leave at the end of his short-term contract in May and criticised the decision to name him 'interim manager', rather than just 'manager'.
Benitez will renew hostilities with United boss Sir Alex Ferguson, with whom he had a frosty relationship while at Liverpool, at Old Trafford, where the hosts will be looking to prove a point following their Champions League elimination to Jose Mourinho's Real Madrid in midweek.
Chelsea defender Branislav Ivanovic said: "It is going to be one of our biggest challenges of the season, especially playing them at this moment.
"When you go out of the biggest competition in that way, it must be disappointing but they will be more motivated because of that."
United's sizeable lead over the rest of the Premier League - they are 12 points clear of second-placed Manchester City - and Chelsea in particular is indicative of a poor season at Stamford Bridge, Ivanovic says.
The Serbian said: "We have to be realistic with our situation and be honest. The gap means we didn't do well in the season."
Chelsea began the season in contention for seven trophies - the Europa League has since replaced the Champions League - but unless Benitez's side beat United or overturn the deficit against Steaua, their hopes for silverware will be over for this season.
A trophy would be an unexpected bonus, with qualification for the 2013/14 Champions League the over-riding concern.
"One thing is more important than any other, to play every game as a final, as a team, to try to win every game," Ivanovic added.
"The supporters didn't expect us to be in this situation this year.
"This is a game for us to show character and a game to react after this one [in Bucharest]. It is going to be very difficult, like always."
Cech remains optimistic Chelsea will be in the draw for the last eight of the Europa League on March 15 by overcoming Steaua in the second leg at Stamford Bridge.
His confidence stems from moments such as the Napoli tie last season, when the Blues overturned a 3-1 deficit in a key part of the extraordinary run to Champions League glory.
"It's disappointing to have lost 1-0," the Czech Republic goalkeeper added.
"Overall we had more chances, better chances, more shots. The only moment they really were dangerous was when they had the penalty and they converted it.
"In the past we've turned a much bigger deficit than 1-0. I think 1-0 is nothing dramatic, you just need to make sure you score goals, you don't concede.
"We will be at home. It will be a different story."