City also showed far more composure in the run-in and taught Liverpool a thing or two keeping its nerve under pressure.
I think that is a false narrative. The Chelsea game was always going to be tough, especially with the way Mourinho sets up for away games. Let's not forget that City also lost to Chelsea at the Etihad.
Because of the goal difference, and the games in hand, they had to go for it vs Palace. Liverpool lost the league before Christmas, or rather, they surged after Christmas, but couldn't pull ahead.
For 2014:
Man City 14W 2L 3D
Liverpool 15W 1L 3D
Chelsea 13W 3L 3D
Arsenal 11W 4L 4D
City:
Losses: Chelsea, Liverpool.
Ties: Norwich, Arsenal, Sunderland
Liverpool:
Losses: Chelsea
Ties: West Brom, Crystal Palace