Micah Richards' second-half header separated the two sides and booked City a last-four meeting with Sir Alex Ferguson's Manchester United at Wembley on April 16 or 17.
Roberto Mancini's side just about deserved to win even though, David Silva apart, they failed to impress, but Reading boss Brian McDermott was still cursing at the final whistle.
"I thought we were going to get at least a draw," he said. "We pushed Manchester City a long way and if Tevez had beaten five and Silva had produced a piece of magic it would have been a bit different but to lose at a set play was galling.
"You could see what it meant to them the way they celebrated at the end.
"Unfortunately, you are not going to get the semi-final everyone wanted; Manchester United versus Reading."
Source: PA
Source: PA