The England defender complained about the pressure he faced at the Etihad Stadium and believes the Blues' heavier fixture load was a factor in their sluggish performance
Yaya Toure and Carlos Tevez eventually broke through a stubborn Blues backline to leave the west London side just two points above fifth-placed Arsenal in the Premier League table.
"I thought they were on top for most of the game, they kept coming at us, coming at us," the England international told Chelsea TV.
"I know I get paid to defend, but we were under the cosh for a lot of the game, way too much really.
"I don’t know why or what was wrong. I thought we didn’t create that many chances and we had to defend as a team a lot.
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Cahill also blamed a packed fixture list for the sluggish performance, with Chelsea facing Europa League performances, as well as having games piled up due to their Club World Cup campaign earlier in the season.
"I think they had a clear week and we have had a ridiculous amount of games," he continued.
"Unfortunately it does take its toll. We were trying to recover from the game the other night and it told. They were a lot sharper and fresher than us.
"We haven’t had a clear week for what, 29 weeks, and you’re expected to go into games 100 per cent fresh trying to push on for every competition. You don’t want to make excuses, but it’s a fact."
Attacker Juan Mata agreed the performance was regrettable and insisted the Blues must improve to reach the Champions League.
He told The London Evening Standard: "The most important games are when you play against Man United, Man City, Arsenal, Tottenham and Liverpool - the best teams in the Premier League and you have to show that you are in this level.
"The job that we did against City wasn’t enough. We didn’t score, we didn’t get the three points, always when you play against teams like Man City you have to perform at your best.
"Obviously we want to win the FA Cup and Europa League, we are still alive in these competitions, but the main aim is to be third and to play in the Champions League next season."