Frank Lampard saw his second-half penalty saved by Joe Hart at Eastlands, before goals from Yaya Touré and Carlos Tevez gave City a win which keeps their title hopes alive.
The defeat leaves Chelsea only a point ahead of fourth-placed Tottenham, who travel to West Ham United on Monday night.
And with fellow top-four hopefuls Arsenal now only two points behind the west Londoners, Benítez concedes that there is no room for error with 11 games left to play.
The Chelsea interim boss said: “When you lose you have to be disappointed and this game was important for us because we could have been closer to Manchester City but we cannot give up, we have to carry on, try to win our games and get close.
“We have to fight for the top four because Arsenal, Tottenham and Everton are close behind.”
The Spaniard, whose side have now won just two of their last five league games, felt that the visitors were made to pay for a slow start to the game.
“In the first half we didn’t do well, we were giving the ball away, we were not winning second balls or switching play as we were expecting so we didn’t create too much,” he said.
“But in the second half everything changed and we had the penalty and yes, it could have been different.
“We didn’t do well in the first half but at half-time it was still 0-0 so we were talking about keeping the ball a bit better and showing more character, and then we had the penalty so it was a crucial moment.
“It was a good penalty by Frank but it was a good save so it is credit to Joe Hart.”
MORE: The latest football news