Louis Carey insisted the Robins were not dreaming of Wembley yet despite Mark Noble's screamer giving them a first-leg advantage.
Palace boss Neil Warnock accused City of being "arrogant" in the way they celebrated the stoppage-time winner. But after seeing their opener cancelled out by an iffy penalty after out playing the Eagles, their joy at Noble's strike was understandable.
And skipper Carey says they know they still have a job to do.
"I didn't even think we celebrated," he said. "We went into a huddle. There's a long way to go."
Palace had the initial pressure but the momentum soon switched to City, Julian Speroni needing to react smartly to deny Dele Adebola.
City took the lead on 53 minutes. From a free-kick Noble slid the ball to Nick Carle who squared into the path of Carey.
The centre-half curled his shot into the top corner for his first goal of the season.
All City's good work looked to be undone when Carey brought down Jose Fonte, and the otherwise disappointing Ben Watson converted the spot-kick.
"At the time I thought the penalty was extra harsh," said Carey. "I spoke to Fonte after the match and he said the same."
But two minutes into stoppage time Noble produced a rocket from 30 yards which zinged into the top corner.
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JONATHAN PEARCE
ALEC STEWART
THE MOLE