Although this loss will be a disappointment to a team who has a long history with this competition, not to mention the psychological blow of losing to a title rival, there are actually a number of positives that Chelsea can take after this loss.
Let's take a look at just four of them.
Whatever your opinion of Fernando Torres, having him fit and back in the squad again is a definite positive for Chelsea.
Samuel Eto'o has had some good performances lately, including a hat-trick against Manchester United, but the Cameroonian has not always delivered, and it helps Jose Mourinho to have another option up front.
Torres was showing some good form before his injury, and the Blues will be hoping that he can continue where he left off.
He did not manage to make an impact against City, but 30 minutes is a promising return after an injury.
There is still a lot of love that follows the FA Cup, but it has to be said—it just isn't high priority for big clubs anymore. Of course, the best clubs want to win every competition, but when you are competing for both the Premier League title and the Champions League, the FA Cup is definitely third on the list.
Jose Mourinho was able to select a team that did not include Frank Lampard or Oscar, and it did not matter as much as it could have that John Terry was out injured. With a week until their next match, the Chelsea players will be feeling good and rested by the time they continue their campaigns for both the Premier League and Champions League.
This time to rest could be crucial in this year's close title race.
The benefits to Chelsea extend beyond just this week, however. Mourinho recently highlighted how Liverpool's lighter fixture list might give them an edge in the Premier League, saying (via The Mirror) "Liverpool only play one match every week, and that makes a real difference at the end of the season."
Although Chelsea still have the Champions League to worry about, as we get towards crunch time, it could really help them to have a few extra breaks.
Man City, on the other hand, are still competing in the FA Cup, as well as the League Cup final, which both take place at the beginning of March. Furthermore, they now face Barcelona in two days in the Champions League. They already have an arguably tougher set of League fixtures ahead of them, so each time they add another fixture in one competition, it will definitely benefit their rivals in the others.
It is also worth noting that Arsenal progressed in the FA Cup as well this weekend, meaning that Chelsea can sit back and relax while their two closest rivals fight for their places in the FA Cup Semifinals.
It might be tempting to say that Mourinho's loud talk prior to this game was all for naught, considering the result. However, that would be inaccurate.
It is foolish to think that Mourinho believes that his mind games will have any effect on actual results. But, if you take a glance at the latest stories from the Premier League, you will find that Mourinho is still dominating the back pages.
Arsenal just secured a good victory over Liverpool, but who is Arsene Wenger talking about in the post-match press conference? You guessed it.
Jose Mourinho is the master of mind games, and, while his team was just knocked out of a cup competition, you would hardly notice. His bold statements and verbal attacks on the other teams make sure that he keeps the attention, and most importantly the pressure, off of his team.
His words might not be winning any games, but they are certainly doing their job.