Bernardo Silva and Mateo Kovacic both missed from the spot as City were beaten 4-3 in a shoot-out.
Bernardo Silva and Mateo Kovacic both missed from the spot as City were beaten 4-3 on penalties after their pulsating quarter-final tie ended 4-4 on aggregate.
Rodrygo had given Real an early lead in the second leg at the Etihad Stadium but City otherwise dominated and, after creating a host of chances, finally made it 1-1 on the night through Kevin De Bruyne in the 76th minute.
De Bruyne spurned a good chance to win the tie in normal time and Erling Haaland had earlier hit the crossbar but it was the competition’s record 14-time winners who ultimately prevailed.
It was harsh on City, who had immediately set out their stall to dominate possession.
Despite their control, however, the hosts looked vulnerable to the counter-attack and were caught out after 12 minutes.
Jude Bellingham brilliantly controlled a high ball with the outside of his foot and found Federico Valverde, who in turn fed Vinicius Junior in the box.
Vinicius pulled back for Rodrgyo and, although Ederson did well to beat out his powerful first-time shot, he could do nothing to deny his fellow Brazilian on the rebound.
City stepped up the tempo in response and created a host of chances.
Haaland sent a header against the bar and Silva missed the rebound before De Bruyne forced Andriy Lunin to save from 25 yards.
Jack Grealish twice went close with two efforts deflected wide and De Bruyne had two attempts on goal direct from corners, with Lunin palming both over.
Phil Foden also missed the target as City kept up the pressure but Josko Gvardiol needed to block a Dani Carvajal shot to prevent Real snatching a second on the break.
City started the second half strongly and Nacho needed to scramble clear off the line with Haaland lurking after a mix-up in the Real box.
Yet Foden could only manage a weak shot at Lunin and there were signs of frustration as the game passed the hour mark with Pep Guardiola trying to rouse the crowd.
City pressed on with Grealish shooting at Lunin and their persistence finally paid off as Antonio Rudiger could only half-clear a cross from substitute Jeremy Doku and De Bruyne clipped home the loose ball.
With the crowd energised, City stepped on the accelerator and De Bruyne sent a dipping shot narrowly over before skying an even better chance.
City kept the pressure on until the end of normal time but could not find a way through Real’s stubborn defence.
Haaland was sacrificed for extra time and Foden spurned a good chance when he mis-kicked in front of goal.
Real attacks remained rare but Kyle Walker, underlining an impressive return after injury, raced back to prevent Vinicius escaping and Rudiger put a chance over.
It came down to penalties and, although Ederson lifted City by saving from Luka Modric, Lunin denied both Silva and Kovacic to send Real through.