Chelsea had absolutely no chance in the game, it wasn't even close by talent, Liverpool had to win to ever have a chance to win it this year (and even with this win its not guaranteed) so Chelsea even though they want to stay in European contention can't really rival the potential champions after all. They have to rely on the fact that in the remaining games either arsenal or man united will lose some points, otherwise its as good as gone for them.

About the City situation, I doubt they will have to sacrifice anything, these people are playing for millions of dollars and the game is just 90 minutes, they should be capable of playing on EPL, CL and FA all at the same time, you might feel tired but for millions of dollars plus a 3 month break at the end of the season they might as well give their all for just couple more games, we are incredibly close to finish line.