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 back line 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. I’d like to not be doing as much defending. Normally you probably get asked to do three or four important things in a game, against Man City I probably had 20-25."
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 the 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 percent fresh trying to push on for every competition. You don’t want to make excuses, but it’s a fact."